m 



i 



ill 



V?.-'^4 



ii^'sm^x 



iiK 



ME(")HANICS OF FLUIDS, 



ttil 






rn'r^'sy] 







I 




ptAiiLies. 



0^ 



MECHANICS 




IDS 



:Beinj ParlTVofthe N4ECHAMiCS 
or t N G 1 N X t R ! N Q l]'H^K9 T tku'Tck c-e. 






DEC 301886 



"iNfove^Z). 1886 . 

Copyright, 1886, by I. P. Church. 



Orr WASHI' 



■,-^°: 






^^ 



'p 




ABLE OF CONTENTS 



3.^ I 



f='^Ekl^A, CHAP, "DeliiVdibhS • FlctU Hrcss^ure -- \ 

^3^/. PtKFfcCr FLUiOd. Z^2. k/c^ouJU and <5ctsci. 3^3. Renr<»t<«. 
§ 3*?^ Heaviness o^ ^Wdb. 31 i>. l>e-(»'iMti^nS. 3*/6. Prcv-ikuV^ ^cy umbat*^ 
^3? 7. HMdYcsIaVic pTCSiUYC . '^*/^ £"<^wi-i!^T<:^s. in -Same ho»iT. Jjloswe. 
§ 39*i/. Moviwg |>i*i>lo>^4. 39icL. Di-alindtoUjCj^s uv»il. It't^uJj . H^OO Co^^ov^twt 

^ i/03. Owuling 5uTJ(u« t\ rw6 -{lulds. -^O^f. rree iuvjute o^ ^tu<i <xt Test. 
§ ifOS ^.Two^u^uLtai m htnt tube . ^06 C,Vx| v>ar«y(:i.yes . V07 BavoixcWiefc. 
§ i^07c<TtW,ou of tiluminariMj <jas. *fC71». Sa^cT^ values V^O ft^TklnXolW 

CHAR I. H^DRO^TATJCS.^BrqUNf >>rfres$«Ye of 
^C^ui^S m TawVs <xr\A Tesewoirs }'*^^ ^^ 

% Htl-CehtYfi t\ j>Y€S^ure, 4-15 ft€iu\tUMlli<fUtd ^yeiS . ov? a.))l«ine iuVJoce. 
^ ^l^. C€nl. <f| ^T«si. i^«<taw^les.tl"c Hiii. Cev»l. <4 j^ress. of c*mlc.*/C,HM4V«^ 
^H-n. F)jo<l (qute. HlV SllAbAiLu o| vevl. Yecl.w^)! wujomst y^^c^ty |>reis. 
%^l^ Moredel<XiUa iOiuUn o-\ ^/^. V5.0. Higli »-na<»o*ivy 4am$ 
^ Vai, e«Yl^woYk aA«.i.TYo)>ezD;cl » ^2?.- frcss, ov, l<»Tk s/6es (\ ji^^^L 

CHAP H. STATICS OF IMMERSIOW A. J» FlOTATiOrJ -...f .V/ 

§ ^It. E^uilibYium c^41olalion~ 'f^l ^A^dyoxyy^X^y . Y^V t^ej^tk of f otdtltfi,. 
% ^'•ll9.T)Yau.<jU o{ sW.pi. ^30 Ant;ulav stti^'ilily d^ sliifjs . ¥31 ^eUcenlre. 

CHAP.m HNjavoilQiVs Co*ihnctedL 5 Su^co^ f U^^b • p,^^ 

^^S^.TVieYmomefers. ^3¥ Ab^oWfe rei-K|)eYara>e. -^361 Cr-iliVrcliotx k- 
rw€en ^a^es ami vo^orb. ^^5 I^avA/ of CVurUs 4-37. G^x^eYal fon^uVc 
§^3^- t xam>les. if3y closed aV VY^anomefev.. ^^0. \f\ar\oXlt% \as.s ■ 
%4^|. BaYo»,.eT.,c l€viclVu.j . H^il AaiaU.c cKah^e .^^3. Work 4 tl^c>t 
expand ing ty VlanoWes law. 44i+. GT«J,\>ic -re^Ye^enWl-.ortS. ^^S\MU' 

^^¥^. 6005 ant e{-(o-rt «4 lV»e oTi^es. 

Lit^twds tWoixglT O-r.-fi £«s avid 'Pijxss - ,^8^ 

5^^? Eyl)€»ime»,Vcil PKenoir»enac[ sreai^iW. -^S'o RecuJiMulanoii , 
%fi;» ^eri.ouH:'stV»eoTe»>%-w;iKeut-fW<:l\i>n» ^^Z first ajjj^l/cc/lTjvi. 
^ ¥5 3. Second ft|>>licaUon . ¥6^ Ori-fKCS hx />im jalafe . ^^\RoMnel*cf of. f. 
^ V^4. PvoWjk efflux, ^^y tfflux lV>vo'oYlfi<^j Uievn. c^evfer.^.'j^eu, 

' ■ I » mm- — — - — - -«J 



I 



TABLg OF CONTEMTS \\ 



^\{\<j^X ^uTiVj vnoitoh , H^\, ThcoT, efp. Hire' ^ect. or\fic«s. V^J.TrlonJc 
¥63. AcruAra'»5cK, mro'vect.orifKe. V6i»', Ov^ilalU. -^66. Fvaucis' 
^om^ulu^or ov«>faJU. ^66. Fbelcvi ex|i€Tm%enls. ^66a. *aViort cyiiw.- 

%m'\. ProU eiMS and ejco\vi(Ac5, ^1^- kossof lieoci lU oYcfices o».d ilioTtl>').es 
l^lS.DidojSliOYlcylm.Utes. ^'''^^ General jovtv-. af BcrnouilliTKeoTeiu 

V7ifi, CKei/s ■jorJr.uifiL. -^.^a.Co^e^.l ;»v jiVe-cu^infi >ioSe ,*^77 Cen. 
SevYotvflw o{ energy. -^7^. "D^Cto . Hl^. Su^e^ eK)ar5ei>»^t*t . ^S 6 
SKoyI K*V^. ¥%:1. Suaaen a.mmulTcn. if^S. ElWowS. ^ft^. Bertds* 
H'Q^<x.Vai^^^^xjcSc^^^To. ^6'. 9 \amjsles , ¥8(> Tl^AH o{en»\>l^m3 ^ri^- 
btal*c vessels. ^^bM..OUicv ves-seU. ^ & 7. OV>«lUk*sVia\Je<i vessel* 
H9% .Tm»e tf| enil^tu^ *^^5- >r^setvo\r^ . ^Sl'. VoWivi e of iyr c^. TeseYVoJa'. 
CWAP. V. }^^lsm DVw.(contm.3 Sl^ad^ j)©^^^ of Wat^y i*k ot>€h cUttne\s^. 
%if^O. NowcftA«iture. 'fSfJ. Ve^ocVry vt.ectSurenv«\iTs. ¥911 Ve\,ux Secttoi'i >\I7« 

*f^5 a. Tw\>«io*</5ct) section. ¥96. Torloljle t«otio\i , ¥^7. "^encis. 
M^^. JOe^lVi'S c1 trtd< sections; lu "(ormu\c<< -Joy vajr*iocL>lc >t»oVifi«i , 

GHAP.V)! '^^MAMICS OF C^.\SSOUS FLUIDS. ^w.. Jj./fi? 
§¥9^.<aTeaa^Fiaw. DOO. F U w tkvo ^ oylf (ce , 60) B^Tte^Ke^^^^^^^^^t, 
5oa. "Dilto J kf^ MaYiolUs W<v;. 6'03 . tiilto ; aji'abahc law, 6'0^ Pv^c^li:^ 
botes. Maif.-Vheor.^low (j( weig'Vit. ^OS. ^Xp€y, Co-e|^S.,orif.ona5|i6YH>if)es. 
5'0^» T^iflgj Wtje dc[(, ffjie\t^Ion. 607' "^eloc. o>| ci[,|,>o«<k "', 6*0^ Tvaus* 
mi6^iou cr{ cor»jsv. aiYjSwail cKau^e lu Ten^. 610. DidojW^e clian^C. 
6b^^ St . i otWovd C)(^eY\\vi cnTs 

CHAP. Vn (^hUDRODyJVAMlCS^^^^^-T.MBeDj) 

mPUkSe aiiaReslSTnWCE of F)-0\DS.^-. V' ^^ 
§ 6*) I ."'ReatTion" ff{ al^txcajct . t\X 'Dllto, 6)3 . h>^)>u)s€ df jct 
•^©K fixed curved vane . 6'\^ T3ilto ©in a -f/x«aL "SolU o| revol "itc . 
6'iS. T^i'irto oil a rnouinq \Kxr\e. . 5'iG. CaV.forma* HuYdy- purely, 

-fWuis.it^JjuUe flmdresi^oncc . i»l^. Wind >r«^^^r€, 6'2o Nuvn^r- 
lea exfivtt,^)^. 6a 1. Re^Hlcmce 0^ still M^(A^\ To hoovm^ laoclt'ei, 
^^,*??V^^®^V ^^*^'^^^^- 6'iJl. RobmSoti's Cctj) anemometer. 
^>§tl3^R€^tance <if sVi^s, 6^*^.' T-r-xni^crliNA^v )iower" tff ^ 



PAR? 
HYDR^\ULiC6. 

i 

3^ L A PE K f t CI \ l-^'^\U \c c^ su^^Ufmct Wit i^^attt'- 
c\e$ <}[ \A'hlen ave ca|5<xb[5 oj ir\u>av\<^ uWvi earn athcv vyife (Ue 
tjVe^tiJsl Ir?e4£?<n Ab^.oWUly wifhc^-d -fnclien^ i\r\^ :^.^ t C^esiiluie 0] 
tiiutUct] i^itVo-tfUbn , I\-^ olkev \^ovAs.l1^^ 4vess Ipefwccr. cny l^^o covf- 
■^.t^w»u<. '^55v'!jo«.x*i of a pevfeci -fiixicl \? alwt)L\|5 or:.e- oj f,&w^-)Te<.^io*i ii^^' 

/Ac Si^yface df conTad ^i afl h&irtb . 

S\€<ar>n otncl al\ gscs^u^ i^a*.^ b« Wealec^ a^ jicvfecl fluids <5l 'is^^il^i^iK'^ 

~ 3^2 LIOU'DS AW13 GASES.A (W c. clef.v-,;i« v.«« 

\»\ca^^\)U IsdlU d| eypa/^Jn^ inl'e <^l5!.>-9er vslt-u^-st- ■o^<^ i?f bei'^^'SH- com- 

^€Wt|5y«s^fei^ai:C{)rGiv«j'l "■^c* The ^^axt w\1r»tn 'fiic eonfunhy v«ss«'l %s 
nw^-Sl ^« p^ daiai m eve^-v <:^,;v«<-U<M'j so ^rev*i»>l lis tSC<abe« 



^ Bn IJEFIMtTlOAiS^etc 

- — - ■ " I I ■ -■'- — 



j\k !« 5 ^liljVit ejftent. l\\us, *t C44,1)4C inch ♦;! w«fcfor lAHd^r 
tK *|}re5Auire of !B IVs. oin «aei% •! ils sjx jflicw )ose$ •nly |tf^ 

Iteiicn exUtvn^ "bflweeu !Hc favtieliS <jrf m»«t lt|u.i49 f* Joom**^- 
"juf»*9int b W c*iis«4#vecl in ^e t> resent conwechon » 

fw^*dl li><»^*s p| i^4t& «<in continue fcv ^J)) oi c«n|*ii«^ i^aec wH»Ui vs 
Ir^H^^^Wm**^ if^fo ^ases. tke r«njs* o| tern j?#»«ture «in^ ]jreS&c4re 

3?^, HEAVINESS ar pJ-^l^^- TVi« w%i^Wtofa, 

4en*ity , 15«*^»*5 ^ Vy ^ ^yaiw^^ «m^ Ij^e voWiMe of a 



9^y^ HfAViMrSSor FiUlOS 9^ 

'ncss^ i(U<e u«^rv dl^r <4yvt4^*vt^ tKe >t«aw%»i«^s ¥v0<a)4 >»^ d^- 



w«« 



/" 



vr«4i^V,5 0.0360 24^ TVs.. 






1 



At^6$)4\«ttO Air 



0.0872 
0.078-6 
o.eo6'6 



cf ^^ViJcK wej^k 0.366 0Hn€e4 ? list Tl/iV.S€C. s^sl*««^ 
<i: Xai'ii^Je Z. Re^M^rtil ftie weljVi df «l iil^t pt^m <^!*«r. 



§3?^ H£AV)N/£SS.t)c.-,rLUiD Pi?£S5UR£. 4 

(rem rt>t failt . fer nitrcury = 8'/-8. 7 ^l"- ^t*^ cu^-f^ • 

dTomeeKdb'iKS Ijj s^Y>%e recent u/TtUrs') we wirtdersfemr^l jl^e yrj,jeV!«i*f 
\CS of fluids QS 4Ati^izc<^ jn En^ipeeVm^, It »^<»y bfi ^wi4«d ih^^:* 

"both me sfc^C^eS 43in<i 4>*'*^'***^* *| ^a^eows {W^s} 

396. fRtSSURiE P6R i/^/lr ARfA.^r iNT^NSiry &f ?Hh^ 
todicofe ^fj yr«$MiVc Jitr- uwif area l>«Jw«evv |w6 c^**t%5'w»»«*i "^ir- 

\a(j vc^^cl li^ j^ ^^c* that tf gIx t^ H»€ 1<?ktt ]frts^^ve oh 
a ^maVl Area «?^ we Wve , ^^ 

i'--^- « 

*«0«4 tKe tension, f« ^^^oWivij ©f oi j»as) ©nt^e ^^-K.^ ^uv- 
^e a/\ Xf ^€$sinre ej ft^e larvae i2!l«)!i>i^^ ejciife w«^a |m- 



<^v >^.5 






^ It^C S«a level tKe oUmcrs|7r»€ve cx^rrs « norm^*! Kresst^re 
$«vi<mc*LW Cause f IwJid. VcsStUre} 0»a tfil ^i^ffet^cS.^ ©j ci^> ^n-liul* 



% '6?6 



HYDROSTATIC PRirS6U^fc 



6 



[wo €iuwcv»^50ir*S *f Itn^iii 

3f7. HYDROSTATIC fF?FSSUV^£jfaR UKiT ARFA^ik 

crr*^ Petwem tKe "I^^Jtrit^ns <jj fl^i^ o»^ D^^^oSihi sides ^ "^^^^ *' 
V^ oO\ cjmtv}iu)4a )Krrti(?HS («•( {li^<:^ -y^ vessel *va5l) ^>c ttiaie<^ 

.i::/j "))«tT -unit aiYea) «*^ «K ^A^l"'^ f ^t£e . Ii.et Hi*. 



tj^rtMir*, 




fie, . V^3 



W?» 



tni4sl Ve (ffl^) ^^<C-^P]b ^::***^ ^ "^^^^***«% 4 ^^'^ 



ij^t^vmrC t^ 



y~^^\ 0) 







&3?7 



rJxnp PRBSSURE" 



qciUt I StrxetUe ]?Hstw Js m eotuj, under tW ^"'*"^ Tb 

4hrA*tf«^ f^ssiv^ (^) we Kav€ p* 7, 







¥A\il^ me 1Wr«£ sUe jWrCS (V^^iC^ 
<SYt 'VtsJ>e«lwely h^rtiCnlal^ V^lji^iW 

m dv4€r What ^g \nl«*»s4y of ^esswre tvt^y )?f c^vY^idete^ ton sX^snt over 
^y onefjwc 5 Ort^ «)3<s Ikiat Hie vwei^Wt ©f me |>fvscw '»%Ay t&t ne^WJsi^siMctf 
\t mv«lvei R?t volume (mrtc <l»mey<S\*on£)«5f U^eJSlisis^ iiv^^ IKe u)W|a<d 
]?r«4SureS involve ^^ frrc a*vtl W **% <:i «i^«remifti 4f aKi^^^ifv «r4<r| 



^397 FlmP PRgSSURg 1 

J, cl^ C.-5 ex ^-'^elF =: 5 Ittt c?/"-f c^/^ = cos « 

^V - ^«-? --,- ^^^ 

^hicli ii tariff evi<\cht oj iVie c^n^U o<, ^ 

,)(ertc?, Me mhnsity cf Jhdd ^r^ssure a2 cLfive7i)K^hl 
is Hte Same 4|z. all'V»<ipnari/ cztlhno ^Icuies cortt^imhf 
7he/ismni, TKU i&\Ke mcsl %mW»Wl ]>rdpev^ ef a flui4, 

316" The IMTrKSITY OF pki^SSUI^S- JS £QUAX AT AlX. 
?emi& or AMY HOgiZ0NTA\. P)^NE tn o ^o% <y{)io^^oQevt - 
<CM% glutei £&t vc$t. If vvic Constd€\r ci'm'hl )fri^m o< hi fWd 

tZiCtillaJ. "^Itftt^e 3<!?j ib lie^se^ Will ^€ V«rtVca? av^^ erf e<|wa^ ^reet 

te the OXiS^ Wve no corvjJDowev*1*^ !l % %& (>K\^ . Tne v^«^t?[ tjf fe 

ftie U U^e^.^^jr^^ ^/r^ ^ ,\ J>^ ^^\ ^ . . . (0 

e^ftuai fd ^at at any Tii^her f^emi^f^l^s The ^tifhi C^/'}^ 
a ^<sWnn ^/ &e fUid */ Stctm toiity and cf alizlltjie (/^) 
^ w^%S^ ^I'amce i$lw^en ihtpcints- 

wh€&€>' ^ty ^re ir. ihc same vert*e<Ml ^y not ^^tid '^hitJ^vty 
he^ ihe shape cf Sic c^r^lainmf vts%H (^rj^ij^esj /^yi^ts^ fhe 
P^oUcf is coj^ttriu&us hetik/een (he ^c Jxfmh § i^^y^k^^^^^ 

M 1 1 ^¥6. /^^ p >i =^ h + Vr. ;^. - h 

K- : . --^^N. y/^ ir i^Yf e tl - 1 -► A i^ ^..^ % - ^ 



*«1^ tK«v\^for e^litr<\xm, fjie f«rc< to Ve ^^rtsd u!poy. l^e )?isj©rt 
<j1 e J vCi, y t*^ ^^**^ Ct»mj^ureoL; For- t/^^]\'hnM^ K - >^ i-^k 
On^ f<,r- ei^aU.ef ])i(oK 0^ ;^^ ^^ p^ -^ /T . ^^c f,^^ jp^^ ^ ^ 

iKe ^otol prCi^uTtS ftn %ur \Vin<> jotcei avc dlrtMy ]>rtf>&r7icn<^ £ 
If iHe fluid: t« ijftseou^ (il) «*>uJt (3) avt bvactviaViy correct if 

Tntn^rrfik pressiore wzlJt edited thie^szh' "i^^tn ev^ry ^n^ebca 
atid lb aQ c/*i2i?^Wtr&.|^Princ((ile «{ kijMal 1^v.c.m#ssr«n <^ Prcssurf J 

39^ N2oV)K^ Pistons, jf iv,c (IcaU ^ f^y^^^^fc w^^\^, 

o.\nA 1V>C vc^^-el wo»1H >*Qicl^ \We Tn-ction tff «hne ^J^ioh lK»t>;<oli A.d»3 - 
lcu\c€ «?^ caK&n the ©lliev to m<jvt lnY6t*^K tfL i^fsUk^te i| <i€l€r>^!rjcd 

t^iiAsilae -ecj<^-*P "^Ut on cMTceuv^t <5f \i^e inevl'.ti «?[ the ]i^»«^*4jO»H^ -fWc • 

l^^tut «>€ aj>j»rox\rv\oJ€lj We i\ fl^e v»idr«en is v<nr*| alow c4\Afll ttieves- 



^3?8 TkVW PfiiSS.O^ PISTQMS y 

•ind lYfclfb"; i'S i%<5t Q|>))ireciaUe in ^Kovt wide vessels like \Ut C^- 
limbos <^ deam- <kn^ oiv^cn^ines ,ciwd IT^ose of air torvi/)*cs*o^5jl 

ar\^ *9.S (33 «ini CO still )v>\«i^ ]Bwxcti'c<jl\^ even wjtti W^li |)kloH 

sJ>e«4As. FcY exAYv*)Je, I'ntKe s)>Afe AB^ Rq . 4^7, Wlwtm Ike >»s- 

'11 "^ ^'^'^ tnov^jr W^>^ l>^e Yl<^U\ Ike thUmity «/ 

• . .. ■' ■ „ , ,. ., „ :> ino ]|3tsfew B t5^]>»a^U»fty edaal Jo ftiat <l— 

3??, AN IWPOKTANT WSTtN^tlOK Wrween gases <^v^V 

A l\<jvctd con ixevl {>re"SS4j£rc og^iiiist IH€ walls 4 ftte CO^jfamin^ 
Vessel onl^ W; \fe we*^ni^ <jv (vvKtvi coyifmgd <m •)! sides) lb>^ TxihS- 
VniUty)^ ^visure ccmifxQ f*"Ct>i without (^<iiM.C to ^Hstoh ]»<SSure,a^ 

A g<aS ^ ccvi^mcd^a^ it ivtust W^ovt oil ^i«les ft Wcv«»it ^iffuSjovi^ 
€xnts "^yessu-ire * en \tis vessel net ohly Wi; ife wcJjViLTout Vcb Iby 
il'S d<3«.5li*cJiY orlcwiAejocy fcs <^|5an«i. If b^-c^Sure jtt>m w»w out v& al- 
so a|>|>Uc£l^ff»e otfiS W a)iM]^v€5secl ©vid «x«iits c^ sl(|lj ^p^eaTtir ^eSStiv* 

Fid 4-^%~» let A&CD^wUo3e aveacx clf^ bd oi sw^dtll «^Wmei4 
1><5f /V ^^ Q. surf ace ,)Jfl»l^« «v cu.we<i5<Hyv4 "^ 1^^ wW- 
"N. /«|\ B % ^f f^*^<^ pressure ^4^ '^»^ «U*>»«*^t^ll^c>t 

^ \^yS \( .^^ ^ touYse norv^o) to ft ,.Itt 4* S'CD k 

n<3r, ■^VS . on^Ut U beve^uAVC^ Jo jind SnC Votlue d{ Itie Cow* 
]>»n€r»t M >^F in ot ciiyechoH 7lorft?Ql \o th\s last jplone (^it^^- 



%^00 ri.OlD PJ^K5S. NON-PMNAf? P»STOMS. tO 




Ftj, M^ 



f^utid ly ^.uJlifymj the mTt>tsitycff tht'^rtsszcht ly Iht a>e<c 

Vestures ^oh the Vistc^n at (A) fCcj. ^^*? U jU4 tKe San. e 

3 -sfeam er c^lr js i^i the Same 
tension . for \V»e su>n df )He 
^rcjecUons of <a}l IKe el<yw*n& 
<5 tke curved Suf jtfuf tff A 

|>Uron-m43iv^ ^e pressed Werc^lW cc^aW^I H>e c^lmdey-vvctU Wi )^e 
^Yctst <x1(?vt5 n>€ rod oY''t4/o>i<nzffr€e^(3 /^S)V5 n.e same.iH 

4^oa.,8RA?viAH3 i^^d' ^.t?...; 

OR xydpai);l{ c^ PR ess, i^ *^" ^"- 

4 ^^e )>nnc\|>l e 4 "Wts^tk^- Li ^ Q 
at^ laave «>J diamctev c?^ TOO. 

5 '''•*' -Xti ft., 



'-.le IKe }l 




E^6r Wqe )>istbn Kali si cljat^^eiev (1^=:: 4<8- CO -fS i*\.^^ "}t. 
TK«: kv^Y MN weighs Q w 31ls,,<?ivic{ Avu^.'qVit (^ ' ^ 

^ ^0 %%, le Kuvi^ at "M . TKe lev«v-av>v»s of %ese fwc^s c^UKf 



§ ^02 



"•"HYDRAUklC PRFS5 



M 




we Have, >«inn^ ^^ z= iH-.J Y. i^f-V- Us. )>er s^, ff ., 
]l«ncp. 4 e ike ],y«s,>nr t«.')t«*«a,fn>».C?) % 3?g^c»^ §3?f 

=• /75'. 6 )ls.'fe>- S<j.i«tii tfv 11.9 atty»»s}»keTeS,<*Mj ftie to. 
t»\ «^j»ifari3 "bresswYfi oil s onl'a^s erf liluHjey fs 

«riaimest l6T©n5(gff < 6CC Us, corJi). The com^x-4-slvje joKe 
t<j?«v. H»e Vjock cyW)* jC ^ *w;i} rr ^ less ^ke we^ki ^ Ike 

^03. TKF OrvMDiK^a suKfAC? o}f Two funx)$f%H?cH 

yoHaT^N^iX)^/^i CO^^TACT^AND AT HEST^ ISA HoRS^aklAk 
F^ANlx, fcT^ K^.US7^\u:^)>^MrtCf csny1w<> joints e avJo 
. <^'"Hi45 -^u^rf^^e few at: cJiffercnl Wel« (^ |>u |rM^^ 
Urc at O *bciwj ^^ ^ lk«i dl e ^ ^ckv.^ IKc 

f«^Y sfciUe equil\ioTit^.vv», ev'^dertriYj Itit lisa^y^Vv -f iui.a nivtst oecu- 




^403 



FRtB SURFACE OF Ll^uiDG , 



f% 



toTTcm ^Fivj, fh^S". '^v^ aucount oj the )>V0Jp«r^/ 
t«4ic?/^ cliff U^ion ^t l^orlicles «[ Two gases IjW 



l^c;--^rr-:i^-rr^ 









JiS^tk 



.^ 



F.^,V6*? 



fovtr> "vnixUire, This ^act gi>;ei sW»wo St4>b<rv« ta t™~--- 

^oif. Ff?e& SURFACE Of A UQo\D AT RfST. Tke 

^ w^^se\ is Ceiled c\|ve€ su/jcice^awid t^ necessaVrt,^ Wv- 
izov^loi (jvovM § 4o33 ^^^^^® l^cU«l fS at rest. 

oi lv6U4;<i T>«lw««H iKeyvv «i*vi Ave 5uvfa?e^^^<iucvv\fi? «J«{r®^'"'^'^ **^ -^ 
1^6|h«s of bre$5«ir« H«t fi^e "jpla^e, wKuK \t coystmvy ti> § 39^, 

When Wf € Wtpdies of I^&m-^c^ ViVe the oc«atv» ^ c^e co«sifil€T««l .^r<nf 
MV ^n no longer lae Yegatdttl a& AcTmj m fxxtalle^ lities jCov^se - 
(^u^eWtly ^e fvt€ suttdce ^f fce. li<^uj[«^ H curved W\nQ T ^0 !Ke cjirec- 
ir©n C'i (a f>}iave Kit) gravity at a)^ Jjo'mts, f«f otdmavy €ia^m«erm<3' Wr- 
"l^cSes (exeej>i in Qeti4eS^) ftie fipeC SuvJAce cj waVey at yestiif»>«e- 

^ds\ Two Liquids (wUkV c^ci>.ot ^-^u) AT i^&^t mABhW 
Tuse <:5pENr AT b<:ptH £:ivrx)S tot«h Air^R^. 46o;>^.4*y 

cjiifc'kcl Tr»€>tu,Y^ joy m-^fewrtce. kel iheir li€a>/ihGSSeS be ir ctv^d y yt^ 



ov 



h-^h 



0, -t- ^, r^ 



y^f OS\ TWO Liquids IM BI^MT T<^Bf. /3 

' me two lnju-wds . Hevtce wc' Have 

?ic+K;^-?*-^\r, '"^-\ '-K '-h ^/. •••• ^^ 

tht 5o{r/«tfe o/ caniAcl arc inverseli^ J^rojae^hmcd 4 //?e;y^ ^es/cc- 
^•wtU "haire from (i) (tneU~]L,- 5ef. i^^^Tem <jj u^UsS 

^^ S3.6'-V 1758- 

^'06. CITY WATER Pipes. l{ >l =• *ert.e«l d.sWteefa 
>4tml X «| <x woilVv Kjse tils^w %f |rce Surf o^c oj fit Y€Serv/jivj«»»£i 

if ^ l^ovwcvtv-', li^e yj^oXky fi yyc?t6'7;a^ IhroujK tilt "^Ijoe^ ftie ]>^es$- 




A V^ fr*^ tVftttHsity ffj'^lwicl ^l^«5fM.V€ d (Itt H 

^€ct^ If vnerc*t>;^ 15 uu€«i JMsleaci <>f vvalev "tJ^t IneJghi s?4J8|j0tW 

^: Uirp tiol^i fK«trt W}ft wate^ >c^>^ ^Ke «^v«ttjayc tK«th«»vci^ 

^'^''•/} fJ^ J*^^ ^^ ^siUv ^ W(?vMeiiv K^iiiyli i- ^K" 3^ |pet k..L 



^¥01 



M/VNOM^TERS 



IS' 




r 



P<«, T"fc^ 



<t»r«* 



C i4 covt^jcleyed the Saw^e ^ iv^ X^, 

Tor aa^-teviSion^ cJv-^a^V H-ian <5vic ottyMd^^jjltn-e^ 
l!\e tuUe tr\a^ Wlefi obeh at jkts fc[)^ {evni*;^?^ £>r\ Op£l^ 

Qnolher Jorrn> e^ the <s^«>t 'm<xn6m«Te?' «Sx?^sr-h ^ '^ 
ejiaw,|.»le, Atemii^ia o^ fXU^.CS' l\os,')>«v t<^.mcli (^f X^ a!i^o%) is 




F;^.¥fi3 




6^-> 



«^ cctvwv* 



^v, LocYom^Tch) r«c^^ V6:^ , W'^rti he 4€v. imc,,,oi,,«i< 



totti^ci^lr 



§^05 



TEv^^oM OF e^sES 



Uk 



^os.TrNSioK or luuKimArmc <5as. U;^ i.s ^M sHVe^ 

sr 4^ D ^ «i,. 4 wa.^ev) TlwcL IS ^ iv*. Rj - ^^K v^^€V Win^ us^«/ Insleoi 

tVte iSa^Ofyxetev A ¥\Ci^, UifS' ^}c He *' fwo ^cV»e$ «r| watev'' ye^<44Vi. 
fee tia^ v»/4\l su]»j>ott m IHe JsjU at B^ Fi<>, ^6 'S'. 

tKi^i Ike ct4$icle «.tv oil « ]«vi^«ovt ^ Q » 

♦oK^tuotrj^^QtitA jr »c \lifitt of l^e <^<i$^«<h4 dti4^\e {K*A ^oH* ^ivc oj 

tff Hie d^ilfiv aW at A <»»i4B rts]^ec\we\y ♦ 1-^ ct*M< J^*' t^ost cf He 
jaS. TkfiH {yo*vt e<^ (!> ^ 39^ we havt 

f^r \i.e warty at A Jh^ ^ Jb*^ ^^ _ (|) 

** " '^ ^ :b jb-^^^^\y i%) 

fo*<5«i '. A -J, ;/= ;^j+ Vj ^- ('^^ 

Tl^e knavv'^ are yb' n: 1^.7 lU^^^tK i^.in ,{;«c tWi ^^/^i^ t= Vog'*^ 

y^ - o.oBoy lU. pet cukfo«t(^§ ^'^'^^>Y^ (^:j3== <?.<:^56o lU^^eK- 



7j 



§Jf££ QAS TENSION 1 7 

is i*a2»^-nvfl[»e fs^^ at Irf &e -|a« %««4 f U«**-0ut •-ilk ^^W^ 
Ff^ , ^6 6 af^u^ s Jt . let ii € w^t 4 Ik 

Q- ^^^i 4^ . ^ <^r%i the t%vo- ^|u^^|?ressuTe$ on &«• ^iis^ ya.i Fl? 



hH4G 



S/^FETY VALVE. PlFf^ 



'pres^w^^ fi^.^7. let ASJk W eiHuaa=>-^^dh?^^ 

t -- ..^..ir^ /r^^i^ file W i5j( ^ c^md^cd %J>e^^- 

circle) c5 fi^ifi^ knjtk Z 4 %e %^e Ww^en W €roiS stctfons^ Tok^ 

i^^^S^S 121^ A.S sk ^ |i^USr€ ♦ Let 7^ ^ fevtSlk iWs ( b**- Ui4t.-*:^«^ 




6 



]f>ro^lMxIny |^\ Tire f Wi f^n^"? 



(2^ 




-U>^ OV\ CtkM^ ^« "^^ €.|&*^e^i4g>T^ 



' a lif^ ii# +■ 2t1^^= .^ ;^ * u-«:^ . . ^-(.t) 

^ Ca:^e I. lf«KC^ ^^ QO ^^ 'TfioL ^^(l) A^ox4^ h^ used I* 
<^r £>v^ ^<««J^ow*i^ <jt4U3i»tl4^ mvcV**! inlKe e4^«cWWvt« 

Oee §§ J9S- W 2o3} ^. ^ (ry?^-;^! . . 

" ^ — V ^ **^<o; 

inkrnot 4itmdar i^ fe «j»*W? w^ler ^ASf^er ctKeoA erf 3^M) |ei f 



.SL. 



^^% TH^CK^is^ESS OF PIP ES .^AiL^ 

^ f T%€^ 4 She^ Wen t ^ jd,«oi72rA + ^» ^^1 ^*^^ 
CSj ** ♦* cost ** i =^ (;J^0047^^^-^ 0.3^ '^ ^ 




'X%?iSy-^€rr ihe €X:j?>Mi}e >w5i ^J^e«, wuc **«wU Wwe G<?^ n*^') 
r{ ft>e i4>€ k. St*)k>iect 1c *• vrolky -raw. ** (% ^a^''^ IKe dirWt 

CCJ/vf^ncJ Vilet ^Ws^fbi' «3t«n>)€ ?) If She <«fart^ aw^eis S?e 
|arei wSk tfe <i«>sm^er^tke sU^V^^est dt€f«3rvv*<d«>vi ^ five nJ>€ ^ 

\^ ccWaviS (3 ^^3^ a ^i<^^ Walvg' to tW lHt»*iW -frrccSw 



§^0? cot^uAP5e OF TorsgS £/ 

Ce.55 of ext«)rnal over "m^ernal ]>rcssuve iS 

(^ l^aioii d cd^ tn same Kv»e<ay unUj^tn wKidi t ^ iK^cW^ess 
<)j iKe wall «J ftie tuVe^ d its cliame1ar,a*i4 I iVj kw^^lijj %t 
erurU )jem«^ H.wdlerslrMoLte Ve So ^uJk\^or\^ (S$ k ^treci^ie a I^caI 

€^c«eie<3t| €^^ VM%T^ /^,7 ^l« int^H«]^«vid 5^.7 lis, orhiYwah 

"pressure ci Ii^uicJs {u Totr^ks o^ neservoVs • 
^io, "BODY c^P ^tQUjiD iw MOTiON^euT )M RE].ATn£ 

"^^tisii^s cive ridt Acii*Qma m€iy reWw^ |>dSiri<>*»S i,e.,are tjotityjov- 

a\ u.v\dleY It-* e \eaJ oj" W J/^'^O ^y nam /'r^'J , \f^\\ eve IK ew slr,*cUy \e - 

\eS to 1^d4i«5 fi»J V^«i in rdoKoe e^M^UlkWu-m . 

Case iT. /f?? ike J^ciyfichs moving ih Joarcilhl rif%t 
lines <^i2'It e^u^l vehcihes^^d <»t^y <j!*;&n in^tant\Q^^^o<. 
'^oXm'K e,\ TRAKTSA^ATIOV), If tfte Coh,vh<7vi velocity t^ gwsW 
W« W«V5 a uniform trc^hslcdwn^o^ iVie Itrrces AcTiv!^ i»h aiH^<»>ie 
"|>aVt««}^ arc 'he^oiv^tt^ <x^\^ *iL w«re not la^^vt^^^ cdt oOl Catcer^- 



% ViO 



REA.ATIVE EQuik,. OF t^iaUloS 



?? 



tcrrvai ^TC^suY^., jVce 5u.yface, {tc.^ave ^e same ois if theli^uui 
^^;eYC at Test . Tnus ^ Fi*^ ^6?^ }{ fte li«^tMJ m IKe mo^*^^ 1<«»J< 

7?^r^fp^7i^ witk <«. U.r\lf<Jttvt veWity^ ftieK<{vu*<^ wMl ve- 

^ui'if ^e velocity <yf H^e W1< I's ot/^celercitecl wA c^ e^.*?— 
stanl acceler^^Viokj ^ ^^C^** s^«>tVol must nfti l>efov%fuseci 







izcntal , R«. ^70^ ;k vvkicti Hie bositicvt of « i6 e^a.fii)U *i>)>li(M.- 
TAe v»-Hertiev Kc mdtion. U un\f. ot/^fel, -froiM. lc{^ tb rl^^l fr* uvtj - 
■foTTv\i\^ t&Ci'xMd- ^rovA 'vieil^t io left, Xet O ^< me lowest Lj/vtt 
k., ,,^£ oj H^e -free iUT^f ace j oivtci 0^ a5»>ta]) Isti^ 

aclyemitu of Ot to ttie l^eesuTfa^e^ 
uifniuhr^ =<3ftlvtoS.^rtS5. )>.et Cro»5 seclion •{ Too* 
Ncv^ since Oo 4$ b€m4 cuce^^voTci iW 4i>eclio»a "2C {li<?»»'*«'^J 

IS col jsrUm nl) liois no vevticcir ciccelcraTioy^ ^ Hie 2 «^^'^. 



" 3 



(3) 



-UjaydJ *\^t.^^^ vessel Via^ a u.ni{ov^ly <^^a\tT^^'tJ ^f^ard 
•>>'.cstK''.i «> a uvu(o>vvtly YeUx^ecl. <^ovvr>»vorcl mottenj (ric J^e ^uv- 
4iK£ v^oi-i<^ ' "be l^ovVontal, W Hie ]»e^swtye ata^ej4ii^?l 

lews J CohSi'de^^viiJ -{ree Ci Snr>«jal v€vi.c<x] j^rU^. ^^>e4c/h^ -n 

C^^eJT^ tlnifcrm kolahdn uh^ul ot verhc^ ar- 

tS^ If li-tfj n^vrtfw vessel \y% F<'j, t7 ! , ^t^ ^ '^c'li <3tvid c€5»uai^»* 

i n<i o. 1 1 Q u-tcL lo e lielH Tdl cu \ kt at a " 
uni'foTt'vi civiouiay vtloc?lY XiT (%^^ 
y \^0^ aVouo Q N.'^cYTicfx] cpcls Xj 

wJU cowic to Ye\«twe e)£juUiW»4AVi.\ 




at ^<xcK |3<j1wI tff whicl ife^? ^, 
imaTl >lVhl '^:iT\%^^ TlIo (ef aUitude = 2^ ^v^d 5€c)io»* «^} 



§ _^fO c;mifoRM ROTATiQAJ 4?^ 

H 4e5ct«\}ii^^ Ci litfri2CMta4 circle aWc«*t 2 a^<l K^iS •*• no verV- 

if tt W€ve fiLirigid \yo^ ^ H^«rf,c H>e forces a^in<;^*t it must f^c c- 

wciiHj'ht 4- 2 , and 5 • cUstawtf tff 'iw CCnrrt ^ <^ravity 4ro*vi O;" 
IrNete P s- 2^ V *^ *^ leucyrtt of J»t<^l . i^ettre ikf ^X ^4lie 

But ?ti^ ^tt^ ot^Tinj on the two en^is «f )hi5 ' — ' — "5"^ 

])n4»Yi are iKeif »w« XI CJmJadn^.^v-iiile rfte liberal ^ 

FVo^CO a,H4 (9.) y^t. "hc^xjt X= O^' ..•O) 

fAtuvgi^^w^tlk 2 AS ils<^xls, Since "rxTX i« tKftjinti^ rcWity T^ ef 

ute jVe^^iAired {We ovd[»v»a.te x ^ <3i lievlicvij^jil dliltaye tff X^ 
f/- *m<A^€S ftdvv, The Qxl^, (^FU tU s«c, sy^«*ri^ Ti^ a^H^fJtfcv- 

veWU^^ -or ^ [?^ /OO 4- 6oJ^ftwi/'<t776 /^ ^cc. p/.B. A 

a.>ial|'.7€V^,,0Y avu|l« <,f IfiO ** ] "Wttii X- /^ ft, <\mJ 4*^ St.*?. 
AnA me l^re^Sure at T> CR'c^.V^^i) t* (Vow u«e in^-'lVi7See,J 



%H-iO 



BcrroK/i 'Pt^essoRE' 



^S' 



he -*r*w 



T^errjQrk, V rtie \/€Ssel i^ cjtuhe "[u}! rtw4 dosed oht4,«>c<4^ 
fit 0*^wh<Tft U to%HVHMiaiculei low ^ '8^<*.> 

^Yce Surface Cc^y\ not hz t»«n%«<l li>^ llie ^rj^^ 
|>e€ .SuY'fate were foty»^^Mh v€>l» oit O 

ciAid wiW te <st re HI 47J^ 

4^//. PRESSURE OK ftOTToM. . 







^ 




2=~J B jfoYccs, TKt< U True evev? tf 
r;?^^ rt>e ^I'ds d^tKe vessel «?%'e"»- 



tvt P%. ^76'^wKicU iH IKtS case(JioYii^Hr<xl)ilafe^kUs «e^- 
TER OF pReSSUREjOr ^)>o;v^t erf ^U- 
iAve-^ *c[*vt<^ ow fine "^^Joie , TKe V>TCscKt (u^se 




^ ifji_ _C£NTRE OF PHgSSURE £6. 

a.W.. Kc aeft-.H= iS ft.,r,=r 2 fi, r^ = ^ f*,>e<|«iv.^ 
4xfc >»•«**«»« ewlVs U1^^, W •uertieoJ t»n*«in <^ the e^Unav.- 

^iO.. CENTRA OF PRESSURE, in <^^c^^^tck^^^^ 
t %€ CBNWh Of p8e^Sl3RG,ma^ W %caUd \>s^ Ike c^wi- 



:-,->"! oj -[ft^cfs ?Vfe^ctc€, cs.in,d Htnce (§ 38 ') Cannot m general be 
'e»i.u£€4 lo 31 ^nq.'^ •y-es^^U.n.nl, but U t ^Vt-'j t^-*?? yoWtt «| «^j:^i6a.' 
Iidn 6] one m Whick ^% a^bi,lTi«vv/ 1 j/??. Hifc -ji>liity«>A/ «^»^m ^ ^ 38J 

6v itaVslf^ ^1 ^. i-^.<?>*l b^dy the iVceS cunifTj ^rn v./V?fci^ mcli^'ie 

^•/3, f?£SUkTAlviT )-tquiD PRE-^$URf on ophite Si^- 
^e fotinitfi^ part ef ca uesscl t^ciTi^ CV CrtiiiiOLhs ^f tht 

\.hnxB.^ or pRSS^uRE. fu^ hii. L?t Ab Wi^^riwa 

vv^3iliv'*^^€Ui<' n>e free Surface ^e^f a»%y C^/% Thc iprc>s;««rf$ 4r€ 11. 

The n^^^vjfti pnSSi/irc qh any ia^/"^ ^ 2^^ <^^ *> IWf 
Sum .f ihese ^ iii*,rTcs^i»^t - f = ^ ft^ P'^^y ,.,.W 
vi4v%iK%«li 5 © iKc Tn^ati z ^i,€. Hie x cf the e^wfve cj^^r^iU- 

^ Q a{ ft")e ]»ktie fi'^i^tre AB ^ ^vicl ^s ^UUl area ^f AB^ 

ei^H<t4 h the i^^ifhi i^GLH uHd^in^^tf ^nsn? ^ fht Ufiud 



f V/3 CEMlEf? OF PR&SSORC ffc- 

,^1 -■ - ■ — — ■ I. n I iMim rti ii i| . 

?<»w ^tt ^urfafe of the 7 if cud , fc» ejiatH^t if tt^t fii^veis 

Nttw let X- tf«H<l ^ «i*v\ol>t the Co-<Jvct^«lc$^iH J>lQii,^e 
^ the >^«>u]lavw. j>vcs«u»e ^^ TK*H loksHj t^eJHr€V5.r£ <»t^ovtfOY 

But ?is r^^ ^ F^^nr>C)Y^skni^ ^t x df«r«y <if« KSi*!«t 
irei fcX (f«e % 8*0 [M.S. H[e etviU ^ l^te^s^re as 

NOT£eSmjr« ft^« )rt*4Kir#< oi-% 1fi« «^mI c^f'V ^mf ik«i«y 
tV C£!r»Rr« «t ]srt«st4re mt^^l lie oKlt*« sl^A^lit^^ wKUk Iftc it^U* 

^/^. c&Nter Qf PRESSURE 0P RecrA^ffikisS 






U 

T ^ 

V... 






8 



Wlnnitr^'fr'hast lies in tke St^r- ^ 







rS 






. ryxt^sl lie tfvi Ihe ; C w^ 2 4 4- k 

line AS from H^e : ^ N ^ 

veyr^^ f* fte n,'i(yfe4 tase (see hr^TF ^ Vl3Jweea^\lj de 



nr-^ 



^7?, we fnci tkat 



4« 

4- 




*7? 



§ ^i s- 



Center <5f pressure 



30 



fM. CEHTER of PRfSSUKlf Of CiRClE: - Sj. 

n TovT 



: ^ Ai =^ 



-ly 



5 ^JS we>)«ve 




V ^y^'KT^-nr X 



F X f X 

' C See €^Xf) § %iX 



-nr 



X 



ielil pre^Suve en tt\e ]>U«ey -J/^^vcre '^cpfH'^S for its \nala€ ^len tV.t 
< ^,* ^^/ 'IS Wli?w iVje vvdiFer* 5uT|kcs ,ttie t~4al wstrc*. 

ev^ wV\^ Ike ^iat'e slides ar€ cencri-we^ ^ l^ edwtjv* 
aleiit 1<5 a sivK^/e "hovi^ovil^l jev/ce ^i tK^- volwe- 
lion beTwe^vi ftie <^ale c^yvd "Jsosts bcin^ f w C.Vo ([aiislyacL t^u»v,yi 
(J'Se 5 ISbJ *Ai^ tvitc^t evf^to^ cuvi cc^wavx^ v€tt»cal force ai lectst 

B%Cilyi^)e 3, R*<ji^y^Jl rtie Kc;n20Hlaa force !E'^f\o ^B2^ 




Ji 



f^%* y//^^^J ^v^M-vi tl^e >uyf<2ice t^ 5^0 melius (vi'e- 



nWk^,sec^ From c^ (t) ^ ^^3 ^ <^.. 

717. EXAMPLE OF Fi-OOD-GATE". F.^. ^•S'S. S^^po>^ 




^^" ( S ^i-'¥ J Coy^sMsT^vt-:^ ' live wWisU «^<:Je ^vee 



i 



'SH-n WATER PRE^S AGWVSr WAU.S ^ 3? 

Wf. STA81UTY dp A VEBTiCAt RECTAMGUkAK 
WAki. aa--'"*''*^ WATER PRE-SSURf Ow OWE SJO^.F^.^^^^, 



F.Q>8^ 







7. r/s r* 



^(TT. 



J ^ It , vficjuJi-r&d Ike Vrol^ev VWtillt 



•*7:#j::^?^^^^M^-fc wo^t^v }res%. X tv^Hst |a)l WilKm the. 

^V<*se 3D^ (]or, ^"hlA omovunrs io frfe sarwc tmUA^ rt^e rvtovwei^t of 

JQ*'<iA»<»J: ^l>^l|ie «u.fev fee f^ ^t wall^ vnnft W nw.tf^«ti*talW 

'Hct wtcte^ sat 5^<? valu.€ (^Cc»i^a*e § J 

L I" 

*- ' Ht^^gt iyt "iiaki^hu «3i^«mst T»[»j>m^ atoul D^ 

\^ -.>^C"T«^t (O^'te a>t exfiut t^u.Qi)i\;y instead eJAvi fv» - 
- L/eoufitlity tl\e Te5Ul\aht K «f f »-i*^ Q 








*'1 



I 



%4l? STABiiiTY or w/Ml 33 

'5'4larit H ^ Fij. ^+-86^ mo^Y cut 3Tj ik 5u,cK c^)>c\y\t E , ^l^<»t 

tl^iri^- Le. iwc TE =- T-J/ i'^ y^V (ov^ 71 > /^^ j. Tfcen idie 

§• 3¥6} vct/v/ e^is the «ydAH<jifes c?f CI Ki«v»^le MND^o^ti ED 
>^;n r: ^ MD J I e MD =:: 3 f^ - 7x) 2^^ The mcon^ 

«vtd he^f'^ Ike mc<^. Ipress, ^ vt2, al "D, Vj^tvij <loMJW)e tKc mean 
ftuil C (se^- ^§ %0\ Avttfi J^^S^ a. $ fife, value |«r llv£> c?Yw6hiMc> 

ihe Kd:u>n, i\e if IP ?^ < /<?'^'^/^*» If -not i' t*,wk 

Secondly^ n beik^ <*§- (?ce ^§ 3V£ c^d^36'X) 

l^et iKe j3Tt^^. J3*v umt Oreo* at ID t.? Ay^ Cl^^ ^^"^^^^ *^'^ ^>«tie^ 



§z^j? STAT31MTY OF RSSER.WftkkS 3^- 

11,3 -bcr M.;ncUC= l^'^OO lVs.>ev s,^.fi.) on fee cerr,c«t 4 P^e 



o 



jt+n-oo 



fc?.iX'o 






I-f v^« n.«V« ^ « f^ , ;.« . i-^^^T? <ut Ike -base ct tKe c^e^ 

olhev co>^ iwKiiV Wvi^*, 1^ <xliWe Too y\tLax HiC coYvier :X) . 
ec^awvaW^ av^d -£"=: 3.7 ft V>^ ^ Cf*^ ft. ^^^0 



^v 



-p 



^l^event ^'UUtAj (^Iti^ / = 0.30) ) )>^ wUk 1)' ^ 5.&?f:« 
t conovww of WcolctfcJ 16 |avove<J lo^ US% 

*^j^^^ } //- / ///)rj /1i(?ia cjf wall citove 5£2Ch ho'riZ, Vcc^ ITX^' ^ 



I 







Vt50 H-!C)H MASON RX X)AMS. 3S' 

4-20. HlGK M/5S0NRY Vmh; mnat^k iKe|)>U=''pe 0;^ 

^^"Ues of stvi«}\ Ixeit^kt (^0 or 30 j^ectj 
^di-ii^'Veixrer K^^f^Vts lVi€ |bY»Kvt!lo» {or hcci' 
tension % ^^ 8^ QoY v^fK<y 'hevc^ ?r<5o/ 

•^67. ^^ ^iw€5 Suck W<J« vo«}M.e$ m iHe V'wer cours- 

es oim wotcld "th^eW coOl ^ar so ^Tfcl c\ T-acLixxl IK«ckneS5 oj ^oiyii 
iti lh<?se coHtSes ^ rtiatl sWou^oht <al^ke$ oo-e u.sma11w hUAt {h- 

,'^<7r eXOJTi^le^ at ol iie^lk of loo feet^wuKeve %t 'K^oslki- 
iC >nreLSSu-rf IS y\^ zz \OoX^^'^' == ^ ^ S'O. ifes/f^cr S<j.ft.^ 
?( Hie are t« Kcxve o. ^ctdtal ^KoYizcnl^xH JKtckn^ss^^^ff 

wJtIt X "hoaovi* T^*!u$ af cuvvatuve Y =: lOQ ^eet we skJl 
ItndL ot corK^sresstoK Wlwe«v»*Vhe\y veYt,^ra4%«i "fstceS of (ft/«L$^f^ 

cnr 10^6 llas, Wr ^^^.tncli ^ foor too <:^Teoi jor sccf eTy evev^ if 
IKo-^. v^cTt nc <i<\v^fe>- of coll^ij^e ^Ike <:iyke Wim.^ sK<7Yr, 
Aiso^if ike Cduyses wert ^ feet tK.ck <3it oOl ©Ikev dejitiiS^l'ke 

lfc5, |>cv 5i^, ft. ^ \6^ Ihs^Y^y S^^Jvi.^ ^^/kic\^ >Ml^'K6 W >w^Y< 

5<A|/t«-*<-vtt A*' (i€£ i%)jiAye^ ^ft «.y<e€4 tKe m^X^ \\eACj\t <sf>A^av€S^ 
"ike, »^ ^iireav»^ cM.llme A C Nl is rviaf^e nearly vertical ^*^^ 

BX))S/ b^ Cc^yv\|>u3o4joVi or ar-aJjK\ccO ivtoj {^ Sc "^oin-Kei ft\at 
wVtm fht rcsgrv/?iy U fujl Ihe itsullant'K ^of jht weight (^ ©f 



»gQ DAMS ^t, 

^^L.J3 \ fc^^e. AC^skoai c<^t The Wed C13 ir. i^uck <^- 

c«^t>x|^«4«'i^ \h iW % ^1^. Uot^ whtn me yeServctris tmLTtf 

^4^1, cx^ CTD^ etd lire Wd \yi '^hi>mt E "' *«» n«fiir 1^^^- e^e C ^s t^ 
ljir«*5ace fjfcss^i^e I^Ytssi^xe tlieye, Ti-»e figure ik^ws flte <^evi>,ml 

Ft>, ^^?. -L -t It H r^qMLiyfiJ to {i<nd !He Ccn^t^Us^ 

^i:^ iFiU « Nv ^^? Wcrrk dam A 6t?£ ^ wK«?«e l^i^^fl 

F|M?tv\ C^j it 1^ €vt4€v>i Vh,ai the h^iZan. catr^nefit <rf JP 
iS Ju$t ik& $a^^ viz.! Til . ^^^j ^^ /^ ^t uf^Ji^Jiress 
i4re W€ft4i^ it dn « vertical tecfanf'ie e^<<a? to ihe Vei^ 



7J73rp7^J€£lion ^i OA ^nd wtlk its cmhe of qfra^yd^ ailht 
3am^ dtplk (ikO Co^^<^yf § ^00^ A\5c 

an^ IS ike €am€ a$ Ike UfoJir pres^idre on tht kmuttiKd J^nfjec- 
h0n4O^.tfp'iajcedaia,^e}>lk^C'^^-^k 

f^ §WbiKt:^ eujAtwsl sWiiiJ the l^nz. eor«).«o. 4 T ^***«' ®^ 
le$S tWm Iht ^Wctten due Vo IKe Wftl vcyI^ci^I '^TeS5i4ife ©«rj1kc>Uc 

?Uw«vev;if rtifr wfiifcv- l«a)es ut^a^v lti€> dam <m tkc $i4ff^*C Af ^ 

ktw^liS w^i^ie from C5*) ^^3 CS)(lVec^U£i as )>»ye e^^^;t.ts) 

Example. (f.ft,5€c?) ^\t\ j^^^^\^u\h^n^ 

as: 5^ ft, a: X ^^'H- ft ,^wd C « 30 ft. weKave tvt^k- 
^nc^ CSl «*K ei^w^lity 5 wMW K ~ ^K^ 

¥2.2, LIQUID PRESSORS om "BoTH S!t>ES OF A 
QATE Of? RI51D PLATE; TKt sluuiee.^ale AB3tVr «>f- 
aml^ty Fi^. ^<10 ^^eccw«s ev |>Tessu,ve^T, ^ fvo»vv VKe /a«A^-r 
^Aj<i/ei^ ^V T4 « 'flivi^S an »|»|j6Sinqr ^jresiute 7! from %t^ fe?^- 




WATgR 80TH SIDES oP QAre 



3? 



ywhevvc^ ^ZX, 



walcr TV. Ssnce IK esc two hoV«x. joy^fS 
^ atrc tJotiulKe 'Saa-Kue line iHoj^-'^ji)-'- jp^vfUi&l^ 

FiiQn ^'/^^^'^ 'Sum J^ lVi©s£ c?{ £ 0.-^3 T- oiLcfil 

V ^AiA<} Cf^ iSive flie Yes[s€cn«j€ centves tff ]>T€^Jure of 'the suf^ 
latces O^B ow^-ui Og'S ^ i:;{vtel It c: disW^e <ff K |roH>t C^ ^ 
wKv\€ K r. i3ttf[«Yev«.ce ©{ level TaelvAJeet'k "KeiJt^ o»iit«;J ^aA s^o^tr^^ 

^^1'^'* TkAn^U^ 6.^3 feet wUUloeare^ C . Hen^c 




•»c%me (ot^t«te fro *y^ its o»»»^ weiaUt^j Wevli^ed \\, K Tl^'iJ: ^ tXsif 

■ - ^^^1% ft . "oebw tfie level ■£![ iht iaiU water Su.'^faes • 
Jj the %ic^Jc'or aof/e /^ cnfitely Ifcl^u/ flif, fatl u/ah^- 



TurfiicJlhercsiUMnl Pressure is' <2hl>}{^ m ihe.cenht^ 4 
^rw'/y ^titt hl^e. PPOOf a^^S^^i Conceive the 1^4^^ 

&e cot.-es|>.mai^ ^^yU^r'yiS 4 tbc 'l^lole,- ** iK^iT s.;v,.^]€ 'mat- 

iflO t. s eui<^v disk ^f 'radllotS a- ^ 8" mcheS iV. ^^^ 

ayovltf 3 ft. belovy ft>C T»l1 W«*«V SMST 



•1 

-4 




'umw 



trr — "■ Izi ?? ;s ^e satire far ^Hy<^f/> /ft iiJoMAi 
.' * hiiZ »>^<Jcn- iutfeore^ so hnjf &s A = ■? /^ 

^as. LieuiJj FpessoRE ow curved surfaces 

eq..*! r. Ihe^ ^um. I« <j eu,«v..l , Ihc S^*U- .. net *?--^^«^^^^ 



\ 



<^rv- 




■ — ■ ' "" ' ■ — ■ ;- " ■ — — • — **- ■ — f ■" ■' ■• 

* "i^ Vv^ l«(t ej^evjuo A^mil (Jmoslmcncfc^^^u- 

ute J . W hoi loflwi ^ V»t i» <3 ^'S. lis ©%v'>^, 

*"' ' cuYUc^ -iuTfacc /s :z:x^<jr om^ is 

TJ^rfHoJ to fr>e S<AYface. Its tirYr»<iaiI Co?yi|5cwgirtC i';S ZL^^Fsm.O{ 

tcJ £-srvi]ponci.»Ts r<<^4ArivtO S*ji>iifv*«lriii£i5lw [roivi vnt oiXtS of tnfi. 
Cc^e^ iwiMtWtVe cacK other. 1ievi£^ IPie '>e^ulh*vtt ItfltUa 

&| rt»e prisjicll^h of the cuLTved ^Lnface u^oh oiji/dmf'T fe 



ar, iiie 'wKole 'y«a«i ^&ci\j\<xst aw^-faul ^ are "V^-uh^^arA ^ Q 'c^v^^ 

l*€,^Ae ?b^«^ cu€ii^hc of ihc nrtjr^}^ vessel ^>zc£ ^^^^3 u/aJir 

STATICS OF ifv/lMER&l^K ^Ki)^XcT4Tlo^f. 
^a^.KiGliD* BODY WMERSeX) m A )-lQUm. BUOYANT 

■ Tt-ki "»€ Cffncci've^^ Id 'becoria€ Tig id wilViowt oJr«Y<^UDV'. of sKo.)?^ 
or bulk ^ tC woujei evidcniW cull "X-wv^siin at y€.%l^ $.,?., ^^!'5 vv?«^«hK 

JJ ^ TtifzM Xcdy- or solud is fminersed tn oiT.i(^u.id io^k 
at -rast^ fht o-esctl&vt^ achm f^cn tI ff{ the lurrouyuLi>^^ ll- 
Y^idt (i?y {tu^j ii a. -Vittical uMu^arJ force called ?k& 'B^i^Y^ 

di'>JH&j,eA^ciyid ^lYif through the cen/ve of <fY<xiiik^ &f [ht 
t^oli4.i^e (^Oi^tide%t4 ct.s 'kami^^necuS^ erf <iis^l<icerrt€yrt (^nciAJ ' 

OF BCOYANCY^nd IS someTm-^eS 5J?okev7 df chs fhe cs^Ire-f 
frojuiii/ (ff d^%}>ixceJ, ujaTir^ If V' ;=: iKe vol<^5^e 0] d^hflact* 

tm-rX cx^S 1^ =c WvtV>ess ^\ ^S '^»^^<fl^^'^Uu,£FFc;^*?rrYl!' 
ec^u.al to Ihc, Wijq^Av^t effort . or if *ls cevjfe €f[ ^y^v^CL^ <ioth 
-no! l*e m The Saw£ vertito] as IV*^ cev»T-r6 of btxoya-^cy^^^ 



%^s^ 



mMfffSION 



'fX 



^»Uen €?f the Wy. TrobUt^is in ill si cH4l«^ ave vcS-tncM fo 
Jf lh<^ C^int^c «f ^vavitv^ \it.<i m Hie Soime 015 jKe f:e*Jve cf 

cert Ire c{ ^t«v, C , 0,^.d if?eW- 
r>n\ ^4^^\ r-1L^ /^^ ConveyS€WjVM«Vift«« w.visV«y« e- 

C^) ^^J i.b) ic) c^^wMid'ya^yU^ii^q^ 

hWi'um ihe W^ W aH/siehecl 'h^^ <::t coy^ to the lolTc^m c-f H^e v'«S. 
A, The tcusiiJn in tVj^s cet^ U S - T^^ -- Q\ At (c) YI 

a^dlh W., U O^ _ q'^Vl^ .....,._. (I) 

ItjiUd tfu^h f'h real uj^^^ht cliyi^int'shed Jay thai 4if 




% 4^2^ a. m?^.BR^)Ohl 43 

I » > ■ ^ i. . I . M l.,, ,. , , . „ .,., , , ,1 1, 

£)(^Vip/£ i. How «jTr«At sx. mass (not >\cl>evir)^ cast iron cwh 
^tfil ef water ^UHi U4U5 cow^^Wy I't^mmeJ § fflc.U>3^^.*] 

iZl(<XYr)p)e ^. 1?e<^utY«(i Jilt volu.w€T , ««^«i Ti«Avmess i-^^ 
Fimn. t^^C^) ^^ (,^YeZS .\ t'=^ 0.03a c*.kK 

timt^ c^S "Hcfliv^f «s water. [Tke V)uoy«v«t «f{oirl ef Hie ciV \«a^ 
l?e«v^ iae«5UtfY«<l «rt ^iv»h5 ftie true wei^Ui c^s GXt*. 1 

^«S3PEC\FIC gravity, ^sj S^taft^avily k m«W*e 
VfiiTic tff Bifi liCovsneSf erf « gw«n liomofijeneduS 5uksr<«r»t€ fe ^t 
<4 A stkniaYii \xfyrvK0j, Sulastanc€|m *tK<> we^fil* Jhe W^i of ^H^ 



caA *uWsha*ice ^ ^e ViMjnr% €YicQLl ex5twt^p)e lost 4ivCtt'|Uu!slY<Jc5 
^ Cdivin%&H melKwi #j ^c)<nv>ivim^ txj>rriiyvev«rcifty the S^«e. ^-jrw-Vt 
4 Ok 'K»tH9^t«%ec>ct< Selicl 5u\>stance , tHe vciue IKcre ©U'ams^* W- 

tA To dendfe S^cc\ftc gtAvIty v\/kick W ewwi€v»lU/ cm o^^Vczcl nuir>' 
\JS 'Keoumt^S l''|^neH*tKe lieavii^«5 d[ <v 5ui>&fcivice wVi©J«^ 

tc^e tf| tf"^Witfu^\ wU^vi IVie loltev c<w. i>« inl-roduced mh Vt*\>- 

vwi^dll\ey A. lloryia^ert^ouS SeV<dL w*\U Sivil< or >«se^ «irK«n HK' 
-m^tsc'A In ^t ^Jandard V^i4.t<i^i$ more easily a)>^li€d^ IKmls: 

"|jWed 1i<juU. W<wc€ ^ , 

wUic.f (5'i5<T'jr , or <r< /. ;tY;sfs- 

s^rxd ^oiscs Are ^w£k\ t^ wov^S o»\ "Pkj/SiCS, 

^?6^ EGUamRiUM OF FLOTATION. 1*> cAse TUe w*l^y 

"T 14 Ike volume o[ d*^>WcYr»er»t civ\J J- tl^e KeAV» cf \»^uUl^ 
^e l»o<^ -nse^ t^^The ^cxrfoce avid ofJ^ CKi^eytci «?( ascutuxtenS 

ceynes Id -rest i\ Sucl\ a Vo^^tion Fi^. ^^'^^ a«^5 Ccvilve af ^vav- 
"ttu Ci av»4l fVie ccrttve of l^u^otucw 3 Hhe h€w S^lwlovvj^ud 
td tKe ri«i^ VoImi*^ of disjjJacevnevi^^vwhwrli is "HvntlW al>d*e \sy itLc 

Ve7t?«:al {JciilM l^t ctxi^ ef ^UWiorr\ ^or line <sf SttJ»}>oTt^ din4 



FLOTATfONi . 



MS 







Jjt.26 

ikal Hnc voUvvt« «( <ii^paiieivicx>t lias ^m-.u-u«Jied. to ^wcl\ 

^^ J^ liie f ^ur.- ^^ vol. A NT), W^w 

com ^Ute *in> m ev s (c ri Hie vol % «f <lw P^<« - 
>Hev%t 'tsvMams consFavilj. for sTible t- 

n^f^}7y/ y/'yP"/'F7'~7^^ du^l^bviHivi it vA essential in ^.very 

^V,oJa"h« leW 3(%e centre af \^^o^cy.L-f^ a? wUk eomfrntt 

wr^mey^i^n^tmee \\ Hie 5oW is i«^>-y»e<i ^ vn<a^ cWo^v^ye ^t^^ 

Th«>^ is -MOW yt<J <^«{imte 'veUtidu Vetweew tKe voV^ 4$|^lace- 
-h-v^a IT ^v^ thc^X oi «.e ^oiy Y'', ui.1eS3 «jc Mev i« X^/r^- 

"V'P* ^^ Tp (/^^ >idi^<»/«<7. s«»)«i^) ***** C^ ) 
The W(>^^^t eff^tt 4 \U Aiv ^*.tiie ^e.ltoii AN£ ma^ \)evi«y, 

^UiiJi? cctUm Vim;U>i4^rtit cei^lve erf W^vj^>.c^ 3 a^e.^^ 
cAx^ my Hie <^«6nidV,cflJ fcvrvt ^ ^t V«V «f iisl^Wemeiit AMD 

Bxaivhk. ft. ^k sec. A seVa w/e^tjhivi^ G ^H-OOlhs, 

^ j^" ioi^^ii wva ^i«at v^.;tk ir~ fe,v or. i^^ ^-.^i^^ft. 



% ^'^7 NYOROMSTBRS 4^6^ 

^^^^ K to coiyt\^aT€ ^ J^et F ^^ev^^le- rt»e ttr''ifi^h«> ?§Aii?a' 

Tr~ -l- l'\oc«Tmf/ ti% woler Tw^^ose Wav.ar ^ j the w«si,IW St4.r- 

Ci fc™ n«oit8H'Jf ik 0{K.olK«v- li'^ou^^ ^ say ]5<«ruA-f:iii^A. ^ -ii^/Wa^-o 

'— ™— e:: "" Q^, c»TtAt- er ^elslK ^Hte l^uX^ st^f ace ><«>vv m^xs-fe'-^ 

Q i$ ftie 5a>r»e ml^otk e3i|*«v»m«^l'S /but ^-ifHile %t V5^ 4 e^«^^|^^^^' 

%Hl^^7hl%e wa)l^ G'-T^ -.-CO 

^•^•T-^ o.«d /, =r -^L-~ .....(3) 

s^slm ^% 1000 -r 172% ^ ^.^^7«r Oz.(^ 3?^)'*] Ifi'lfi C 

''^^ 3 ~f OJoX-y^^'^^^ ^ r: J'6,7 rJ.>eve..k f%d. 



I 



%^2g. 



:t>BPr\'\' '^f FJuOTATioM 



^7 



hQ% BFPTH Ox FLOTATION, jHie wti^^it^xvd «^tir. 

d4!k4}ht lomsi ywt Wou.A.t ^^4^e may k ^el?r.^.ma^. 
(Taie J Kik^t pnsm er Ciflmder coA its ^iS mheal. 
fni. ¥9 7, (Joy 6lat,1ilL m lii^S pasirio'n See § 4^30) 

i»^ V t • ^**^ secltoH (fai circle) ^V ^i^« altitude ^a^.^ \ 
C^^^JT, Turc^rnid cr Cont cu'Jh <^x/$ vertical <^nd ff- 





Case TIL, Ditto lul vertex up, R<| ¥9r, Utikn^b^ie^n 









F\^. ^^?. 



^"=f.:4'-^=^^'/^^'-^ 



% H-'2^ FlgrATJOM. ^ 



»» « «''^ 



B^ Ample h A 4*H«T€ ef ^ mckeS aW^^Uv !S ^^-^1 
i% htjcwiness (3-^1/* vH*A^t]?e sr ^'-i- "F ' ^ g^-J- ^ -^fr" 



%¥i2|^ PXMi Pi, E 5 OF FLOTATION . ¥t 

I. . -. ■ ■ ^ .. , — _ — _ — , — I ■ ■ ■ ' ■ .. . I ■» 

fey) 4 0" «: 0.30 . Ret*-Wea tVtt ^e^ <jf fi.4<^io^ 7i. 

Far «<-7i% W3?/^^5A.i^3''=<?-?3i3 
^2?. DRAUGHT OF 6KJPS. I«att*^5a*l,;i,,es>«- 

t^Jdli^ >f ci| a new yHd4^ , %t Jsesiftors «f llie <*mWe if <^t«ml^ H |«MUftd 

Wi) U iWi«^€i % il^e 5m*?^ 4'^^»* vuei^^th^ «w*4 fee <|Mje.ii«nt J 4 tkt <ii5 

TiTi^st two cd-oT^iwaie« <ft»wii ItHe ^t thai ftt« <:«*i.df ^v^Tic^'m 
feg r»%«^tj3i^ v^vfical l>lai%^ of s^ji^TrweTry cf tW ^hs^ Qtn.^^wt^l^ g^ 

l6C«Ii«V*« TJsgKlAt w^i^kt ^C ^ » d|co*AVSi, t!ie Sum a<{ rtiie rU" 



I 



§ ^g j DRAUGHT OF SHlPS S'O 

tih/e u?dfsvJ?#?€ 1?U?^€ a»*\a the CiJelieA surface ^ "VKe Viuft* Tn«l 

^ fe t^ 4 Wa«»%l«J \amJy^ae erf e^<<:a2 thtchieSS ocyj SiVw}>- 

tnwiftc) cim4 ols^ (<^, 3 § 5S3 if^^ 'h«i<j)i6 ^ '•l^^ ^ent.ef *^v^, 
dA)^?^« H\e "keel , St^UifcoW l*^ cliVt4>toH ^^teNVem S to 2o)vfr' 
twfail s\t«es "1 io keel ^ (a»» <ve»n w4>*,^-er <>«h4 «f e^tcdt/ iht^^^'^ 

^r ftni ^^-uiitWiUsvi ti stable «r uws^Ue ^ee ntxt § , 

In fvrff^ *i^»f>s Ike <teviRe ^ <j>«v,^^i 5cve*^) ^et, <*k«<^€ %i. 

*ihr$ *rt»j ^nt ^€|<pil's «t ^iiftn^wt ear^^s caw cjso ht ^titsured. 

^30. AN^GUUR STABlliTT OF SHIPS, ]fa tt«d {^n^ 

u^JqKl ¥f«Te ^ H»t. )>*tuliAT "form fl^v*4 ^sUuin (?f R^, SoZ, (W^tr* 
^ \y^ ^*^ *® ^ action oj Bte CC"^U y^cw '^ 



0B 






I 



I 



§^30 



STAeiLiTV OF SHIPS. 



51 



«{ iHe vessel fl^y€ ei!^* imwe^^ecl ^<fv -v^seJl d*<i «({ iKc wc^ler, 

■p?%yv flic vtr&eal ^ F*^. ^^^^ lHo€ t$ <^ ??<?«; C€vi!>e iS^ huxnjc^ty 
"^ /£° ^/ J) Cd»r«^y^>Hcimy te The i^ewv ^a^e 

"^ tn& reverse) cs*v&Uts cf fr»6 ^6 ^orc^S 
tnent erf shhihTy^ <ff ^ 'yolw.e (3^3) 

'^^"ttjo'A }W« ^fe^WaI avid Cb]^ff5i^e '{etfes^^ewx.K ^ "Vl- ^ <^y^0^ 

^ P^>} -^ i^ ^i^h^Tf '^ s.^. =-^ Bes«^ +V^ ;;:b*a^ 

j§33^340.-^^^^-^^^^^-^^^^ ^^.^ 

But Tiie c«<4Je r^^PJ «^«i<i ^ Ht« •n'k^ •ti^i To -ntfkt Hie ve^' 
S^ >| n5 vi«»^ W Wis of RieliM.l\ *WlcY<ct tVie woTev CV€ir«Aerj- 
e4 freiv* it^m.rtse Hvilmcc^ ^o^iti^w-jj lv«nce ^e cJfiey e««AJJe \P V|^ | 
:^«'* \Cs existence ^o tU« ervvCY%4«n e{ ftie vweije Ao A, , a»^*4 

ne t?n?v?«Ts«on^ iHe v^r&ci^'t MO^J, ji.e.^'^fe ft^e loss <rf a l»u- 
O*^0int ^orte. Q tr (y«l. AoA/^V' cn «v»€ Stele Ctvul tH^ ^«\iWd[ 
otn ei^fe^ej l>wi^v|civit |ov<e cw the dkev* *\ thtS ect-^1 e |T, ^Tk I 







^ ^fSo ^TABaiTY OF SHIPS A^ 

f^^SJ^ ^ ^ skf j^< e^^« 1^ T^ci ..,a) 

•nat >*e£Jti5aartl^ lie «*^ Ihe vjev/ waler-IIv?? ]>loi»t€ A,N/ . 
|r*w ihe v^Ii^<^.^n ^a2r water ^ f«r wk«isk d^vt^U tht w<4^eS 

fi^ . ^ 2>eivt^ ike otWi^r^cu^ |i>e Cwyue etRiH- 

is z^o^afe»«i jet 4» > OK M IS ncyalive^ m^^icc^rmij a^ up- 



^3l/M£W^NTRje Of A SHIP, l?4e^*^h fi,, 

q[?dLV% C e[ the sKtjj, The lo«alioii «f HiiS l»<Mnt 777 ^Kowt^-es 

CI sftiyt floaTiHjr u^yioUi is in siahie efouoi^rfu^H'ffd^ 
nfJoc^enire ^ ak^vc ifs cenHt ^ ^ravitu^ofrktA viec 2/€tSa ^ 

>out. C» To -fiKdl rttc m*fe<€»4y€^V^ m.«<3m^ cj^ Hie <itVJb«tf t^^ h^ 
'TKent rV y j CC 'sz rtie $u.m of lKe iM^mev^ts ol>^wjt 1^ li^>»z* 

4^«y{ ftte iwfe*V*^ s«cWn ^m Ol^(j^/K{«VitS lite ivtltyKc^H 
??| l>»e tvf© waW\?«".i;' plashes) E<a«l\ ^/^ i5 /fee W-^e of #% 



I 



%h-Z] 



MSTACENTRi: 



_ . . ^_ 

C^y <3j{ *^c%f2 A. Ok A ^^^>^ ^ i^ ixe^ottWN 7Hc Wi4.o;5<^wL effort 
^ wuUtck I denc&s liW >vicnv%, c{ me-ytsii ''^§ §S^ of Oie pane 

Ki wkick C ^ ^C - <^tsla44ce |rowi cent. *f (^r^v, t«. fte cevfr. /»f 

bvu»vancwj ff^e hci^c0ws ^law fccivxtv ttsed xA^Uew C i^ •*l?ove B «t*«^ 
"V^;5S vtfKdle v<>UuA^€ #f wafer 4isj*faee<i \>y In© sh*iJ3 . We t>Axu^ 

flO^c wTile j-{Tfi>»^ e^s. (6) o^^^c) 0) ^ "fdv 'St^<^}I Values of 4> 






H<^X73 w«*lj jfi»e n«^v cit- 



-WtmS 



Ji^ 






^"''^^^^^ ^ic^^.ire ^ i^ ^ Ci,u7 5 c c*Uve B "ft^c cent 






t3i ^s'-^bHtce ^ li \>$]o^ Jl^e vvottir4»n^ 



Fi^, 60S. From e^(^) % ¥a^3 h:;: '^'/^t 

ftv^ smce ClD = ^1,*^ c^4 ^O ^ ^ Ji ^ ,^^ ^ _ i-(V-\) . 

^n AKf ^ ^ rv ^ Abo T"= vkv^ yi'^^^4^5 



•i 



I 



« 



i 



9 4^3/ 



MfeTACEMTRE 



^6' 



One <j( 5We<'][^U5a«Ka vice veirSo.. E.5.,»f }^ c^j^j o*'^ "^ 
fig. 6 0? 




.^ /iO /<.-*'-* - -. ^ ^ ^. ^ 

itcuf wflJfer-lme Sectiow eff a )«xd€d sK»^ <f[ Q*^r: 'VVr 800 tsH$ 

"^rt Cff hccayarrcif^ i.-C . "rviB - *?• (jfce «^,i*utjt W(«t€ c<^,(6^^ 
Mow l^e cjiAAwiily I cr{ Hie wat^v Ime section %hcxw ^"fVo^vi S^^wic 
rncFr^ (see §.93) ^e written J cr. i^ (^ ^ i^^ tSX 




'"r4-~f^^c^^^>--)+^o>V"^3+^:] 



TtowH wV\i^^^ ni«mcYlicci) ^uV>iltCvtr«oii , S^e '{•^^ ^«r (^iwCw^iewS .tt JC" S^ 

3X^ L "* 






c: |f^o8c) btWlfi. *;^~ J_ft -J3£A£l^ 

r See ld>ins£?n5 C^c'loj>ae<lict ^ arUc\t, HciVixt O.i-ctnteclu.ycs 

lic:jLu4s kcvs^w'iAui Ce\Taivi limth, tut TiHiC influence or, 11^«iv stal 
Kol l£>eKaywJVj\>4*t w'j^K ja^es irtuAt alwa^^s U Taken infe acfdttvtt^ 
*iir.ce tVi6 ftty«e <^u^»vtull£^ ^ ^77 5;oVz ]'emhcr<z2Ure J cm^ %f0ii4mt 
c?|3Laiv«vi i>vfi<>ss cf qa^ are cor^vte^Ied 1?^ ov TveooU^ 'mvAneibklAw, 
«^ wai U Seen, • ^^^ 




mhT^4xl frtmatKe ^lowal a\Y U4. 
«J wh^K <\Te at <l liMSion ©f rm^ 

\-\j jce (^|re^t|n<J ^mt^ tVie fihr^l^ slants <?i i<f*vte ]>#iv»l: F i^ trie 
licctt impovleci t© 'it. C*^ke qUss ctl^o txpAv*4S^ljui otilw <hLo^ 

I : i4o lii OS \v.uc}? 5 iKi5 will fe^ v.^l«ct€a3. Tkc dishoxce FB 



^ ^32 1 H£HMCMETgRS S7 

al<5vi^ thC' t^4>e tT»<?iv^ now W Avid ed jVio ik ccnvehUnf. rvur^Wer 
4 a^MA.1 pift^T-S <:c:»^le.4 ^k^r^seS , ff inL oj-jc Wn^^rexl ^€ftf.^s^i / 







dinctS'^ litriik^ Soht^j^ OfS |^ isfhc same loiit ^'i -frf^jtlZ. isihi^ 

r: seaJed at m^ &\AtY cxlYtU'Altij ^wtlK <k vdkCM.ui/i^ ai^sve ^^e i^eW.H 
df me <3ur-^Keyw«arvi4t:«r- 1 kal cc^iA^J^^vti-'riv^s^h <^f, volume t\wdi 

c^no * .^ '^^ '^ »/-*' €^l I ?>ui vj^t "pT ^'^'^' ^ V" , 

}Uc&l at 3'X ffi ilnese ^.-xrk Wosfj (Ke ^'^'f^.^^W po^J. ^ vvK^cUt^ A 



tA^€ 






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TfcM PEP ATURH: , AftSO^OTE 



58 



C^>il. •* ** '* PeAreythejt ^'^uli.'hy J^* oi^ «*^ 3j^ • 
^34^. A8S01UTE T^MPSPATURf, 6x|^W.enl cOso sUs 

fttftt >f a •*iAib5 tff ouv at d8>er perfect ^os ^ corifmfici m «\ve^sfl 

T^jrjami OwsG/i/ J w&uU \>>^ tU tVt^teahdVtS Serve a5 flLlberMcvvieJ^ 

F«'a Sit aH^ I^C atfatf^*^! ^eJe c«>ul4 W' 
4hr<l^Ui3te<^ otcfoc^inOfY . I kw5 \{ Hie Cftl- 
i«v\V\ $tocA at /\ wl^«vi lU^ i^rviWr^T^ 

Ike CevtVv^^o-Ai^e SN^sfcwi J «w*<l ][V»e ^*^fft 
the <5c*5*Teviswvi w-tx zeT<» wooclei Ve Kt.avk«^ —^273 Cent, 

a»^ "^KiS J tn lite Me^T*»HCAl "Xkw^ <?f K^at^at TKetrHcJvTiavnKS^ 
^^ '^e Qhsoluh Zero df Ifettif^traiuY c ^ oy^A \^j -^^^Ufi^y^c^ 

dered srviux-k YROYf simjiAt c*n^ eovv.|3<*^t, Tev-s^J^frcsiJHre $o >^^ck.cvt' 







^Jl 3¥ QAS^S V5, VAPORS $9_ 

/yi kna^tfH justs ««iwlx convey feci 1^ ei Svcf{iete»il r«<iu,«lUn <?f 

Itr^^en^Jc.^Hftii'titJ WfH •nU TrecfvilW (^S'l'Sr) -^cdttfed tc tWV 
Avi4 d«<$ H«t skovw IW. r€^u)a.vVW tf{ laeViavioir uurtdtr c\tA*a«5 ©f 

4a^€ . The ^l«*wm^ ^AU tHu5}TA^e he )nro^ntic$ «f v»}>ot-S \ 

TK«.§ Httmnt^* i^ O^ dosed VACUOUS 5|>ate ef em5}<^e-rftWW)ciy^. 
Fid Sift. ^^ V-ajj^T C«SkS€5 to '(oTvvi Vut>e»i ftic T^ViSl^H 

heai b^ ^v«ulua4lw c^^liect 1^ ir«.fS€ fee )ty^\^tr<^tu,Y€^ft\oyt v«^<?r 
wiU -form (wiUt AtJlittfH^Uf* fr»i»» tk& W-. <ff fte ]«qMA«^;M*t}ess fte 

a /t^^a value pr€a£h lh^fiemiur<f ^a iai^j as fhere ;& ^*ty 
F^.r,to4^ ^^"^ ^^^^ Z^'^*" ^^^* ^^^' ^^^'^ ^^^O*" 

t«S%'- ^-36 o.?3 3>^ /^-r /7.^ 6-5.0 67. 2 




S.«f»t 



I 



$¥3i' m%^S V a VAPORS. 60^ 

will 'h0tf9 httm «€rm«r^ «nl« vAJw? Q'^.'Jicmi)^jmdlj ifee Rm^ 

VA^ k 9i^w §^^ 1« Ve $<^b^^^S4fcl^^ a%^ {^sTTm'g TH27TC «>« sis 
K^^-n $^«%€ cy{>ar«««»«t«b ^&rt teems ti W two^^h h Wie^c 

vev»^ ^if «N«j T«««ca«if«s c^^ ^u!^^^ ht^ ves^ «&««tj €»*ea^ 
lake ^ ft>« ^»p«SMi , *T\\^i% <3iW%c tKe ei^^^ l^e^^^cwlii^e 
^«^se^«?ica4»o«Ue «( li<|**.«|4i«fc»i Vj J?T«ss4iy€ «l^9^& ^wki^e Wti^ 

the 1«M^^o^4 ^0i»« W WtSadL 1^ Ike vo^«. ^^^^fr^^^^ismd^ ^ ^ j;fc4 
^ «>«A*i4.j Smcc 22^* H Ki^St^ %eiM. lie lt*H|». vnkftck f«frt s4' 
til Ike |r^«^3, ^ V&*3r44oW ffJ^'A.'W^). af S^^'' fiAn f^s- %wd,' 



I 



i 



g, ¥36 kAW or CHARJLgS _6| 

ht^jotr<xTt4.ye^ %^ V€YN| tow. 

^36. LAWOF CHARiSS (AMp or GAYXUSSAC) Ue 

i\ov\ ^ Novo ii73 ^eCrv,.^ the yeclj^reecd »f •00 36? \/utKi.oiv 

•f Cent. E<^, (^5l) 1$ ojio True wKev\ T «*a*4 T^ ar< tcHi €K^T«s5to( 

tW ^/^c brts^uYt ycyyiainth^ /he ^otme^ /^e valurrie of a ^fvtn 

o*nce tV«e we>Ai arf the ^iv^vt ^w^iss ^[ ^as ia mvAT«ciUe^<sAoL. 
^^»er^ ]>)«ice ow1^« eatlVi-s ^urjace , w#t wiot^ 

JjL, z: JS- ^..... fjress, const • * C^) 

>- T ' 

».£., // Hit Jrriss, fi conslani^ fhc h^^^M^Ss (cincf .'. Ike s/fceif- 

Ir>fl3^ime»it ol^d ^VvJvoS %V3V, HlAt^ifilic volume (f%%*a^ •*♦ 
rt»t. he«v>iViess etf.3 j >tvMAtvis con&Rinl vuWU VKe remjjtvai'Ure 
v<5iYCeS^rt\e Jev\siovi !> vvl\l ckcHv<.ge accotts^vho- liie -[ol)ow»v*& re - 



^ ^S6 LAW OF CHARUES (j-ft 



D 



i ^ci^Am^ -Hi* Cent. t<»^|% *\ 1vrtn^m»iv.^jAi be 

Ct^ tht 'V^uwt.^ <3tW hecti/i^tsi yey^ainrVtf conuaKtc^ fhe hi^s^yi 
afoi f{j€K yuiciCS varui dirtttl*/ 4s fhe abSci^Je ftiryij>craitute» 
Ifm^ \% coined ?K6 ^AVV OF CMAair^ (or of GAV LUSSAO 

^A37. <38NeRAI FoRMU).Ae foR AMY CHAnGS or STATi- 
Of A P6Rf8Cr GA^, If *»ttiy 1wd 4 l^^^ ''^^^^^ cj4A^*,ti'neS^ 

<:\•^A>^acd^ tKfc value. cr{ Hie fVi^irti i* defervk^mare -f^wt IkoseTwo 









r. .- c 



/^-^ *i T fteMiCi^^ JCCt4>l€S <HVia1uv«€ V . 'vCo 



f- . » 

i»et it v>c3wV>c n<aW, without cWxxvt^c o{ volw-wie t© <hvi ottsoi.iCvHi. 
€M 1o oi value > ,sucW tt^^i 1 ^ - ^ (t) 

/itVv<46H |4 P ^ VoliAV^t V - Ot-'Vi^ ^$ok ^evv<)J. *T J IK 

GENERAL J ^'^^ - ^ ---~('.0l 



i$ Irvce -for em^ <Uav«^ «j state. w« w%<xm aU© wt«te 
(CEN-£m>^ - A. ,..,--.<.l5i). c^^i^ ...(13) 

/m *tH /*^ »^ 

Tncse 4i<H<^tuMa5 (5j ^o 03)^rHr)u^., W<J ^oo4 "for <*w s2i>^ 

%Cr^t T^CYS Tb The ^We «( «*^ A)m<^, If>»Sio», ovvi^ \rtet^ 
yoMftl toT«^cJUjrt * 7M <vvmJ ?i r*^ any tu/c stciS'eS wKa1<»- 
eir ('wVBwu. }n^«cTifa2 Jrmtts^j j/' ^s%t "Vieiscvmrss §§ T^i'^i^S?^ 

^38 EXAM pies. .f>ra^/>?€/. Vv^t*ukies|)ac^w;nW 

w#"hftu<: yb^ tr f4^,7 %s,)^ s<f. tVicK , ^-^ rr n<?(556 T 175V] lis, 
:ferr c^ic a»«i T - i273 "" AV>s.Co^.,\vVi€v, HUe 5<;i^ k ^t frtc2- 
it^v. p>»Wf*^ (xt tfv»€ at*vt<«, (^ie. 4n Stofe Sui>-2<vd)^ Jh the siole 

T=^ 273-hA7s=r 30«?*AW.Ce»,t.,vs/Qe ^ U re^niv^. HcJ« 

^>s,)>e> cuV tU «= ,0>0^ lU,ye> cut.-f^ct 5 «Ki '»{ Hie U^l v>fei<jVit 
^ ^"^Y ^ ^"^ ^ .^ '^^*' uue'k^ve^^fiakseA'Yi il-^oio^ 

SxQyrthlt 2 . A masj df ^^Ur ong\«vOly ovt <V* Cent. <»v*^ 

vI^b^^^Ki^ v^i< coil tKfi sl<3ft^e *n , l^rt Vcvi^^ IWe e^^j^ma) slate, 
U^e the i/jch'lh.-s^, "^A^'eWae ^^Wci^^fKcrrforc 2? -r ;^^ ;^7 



^VS^ EXA^MPXE5. PSRrsCT ^A 5gS 



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rf T = ft? 3 + SCO = 373'AU.C:^ 



{•i he. wvt'knov.-n c^w.ttvJt'L . FV»i«^ f-lSiO) ,'. 



.'» -^- -vf T"^ ■^a?7 30^ 



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fU8 ^1 clc>s€d vessel at oiXt¥r^\j,oi 16" Csvvt, ^"= 



613 



ot))«w%w^ (X )>CTtion «{ \\xt ga^ to e^^^t^e 



e^^^f ?.6' dWs/C^^^A^i^^c^ tm*»ecKc»)tls^3^ lis tew,.}., can net b^ 

^la.st we shk r. ThtV.U. sec. TW V^UcU^i^-sUviii^ %us i 



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y^ -? 












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§^3^ £XA^4PX g^. pgRPecT aAsgS. 



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^'^ X K T^ "f-Km Q9B 



^^ftie Wof KeJ'*^'^ ttH^er ^idi^evt wwi|iTg?siovi)| ^te !> ^^^ 
elev W WrteA ^^ sWai^t tUWe 4 J^^^,<^ t^nlferm e^Wrte^ 

>,** ^ ^o ^wi <W to t^e tvxercuiri^ Coii4i«n 
m W fetU mM$l «lt^i W ^^ ^V^ ^ew,^- 1\ ^o^dVu^ vA^wxC 




tube *^ 5«re Xiotcr?, b?ct4 of u^v)^»^c?w>x t«wsift« ^^ l^em^* A<iiWi6» 
— T^ Ate UeiffKU A A**<i ?•'* are ol) served (^Ufli'* definot 

wV y^%y^^^ _ . oy 

tn. wUick 2? s; IJKc tev^sioH erf iKe aiV m the tU»e , 4fliv»x? k-^ Itia. h^av- 

(^vdl T^ ([N»6. T avuA T^ Are Oihsi^lute '^loij^cycttlttes) ^ ^^4 e&n^ 
1» J<3V eiK^ vaWtf^ ^ ^ J ^*^'^ ^^^ ^J)«c\<>cl value tf{ T, 
n^a^dweW "le t* Qn JrttfK It. S€C« 5y$^ ^ =s lf*7 (or ©ud 

^«/:^4«.<»W T}*^ 7i '' =1 2-S* itt^UeS <5»/'Vt^ ?l "ST /y indices . voK<vt (tiC 

tewi|>. \S ~3** Cev<l ^ ov T^ ^7^ * '^l*** ^•^ . Pot* >vt«v«Kv*^ 
5 5 fa-vcrrtu c^ rHelf J<rr cAck Cent, elcjtce)^ H^^^^^^.^j 

^ nagr ^ M- 2^6- p , 4 

^HO, VIARIOTTP'^S MW^(jYB<j^V5^THNlPEBAr(;R^ 
Con *dTAmT, ^.e.J5c?TH£R)^A)^ cHAk^^E . rf^^^^scf 

^<^5 )=€ C(?v^t.^e55irdi ^ OY <5jlowc<J T© £xj:>ay»i:^ ^ /Pettier r>f^}iy ^i^t^ 



ii 



i-vsaTiovt tv%u*i W slow) «^| Aio) «f % ^37 -n^vv Wvv^es O^'^^^*'!.'*^^^ 
(MARIO Ttrs UW^ ^^y. = Tl> . ovi:! r 2l . hi 

t.«,,^e UH^jxraltZft^ retnoitriiyif axfchokfye^d^ fketensjcyj^ <?>€ 
muersely ^raj^yti<fyf^i /o the val*4,v*<e^ ^ ^ <^ ^we^^yvta^'i s'f <^ 
htif^cl 9eii,'y or^ fkc Jsro^uct of vclu¥*f€ iy hnSim is a s^n- 

I f*^i" *^*^""' -* /^^ A" r^ /-» 

ue. A« brfssur€^ (jorlt^uons) <kre diredlY prol^cyhoHat to the rfi^'si 
'fjau^ey^ djj iht htat/in^sse^ ff like fen^. }s the S^me . 

^AW Two ^uv»<it£<i i^ear^ ago ^Vut <5^ UM\%e U ovCIy A)>aiIi<uW «^$^ 
<j( fine o|e»\<tcJl •jortv* ulo^^lav <hv\y cWv^e ff( simile, m ^ 4-37. li ^-^^-y 

^H \b o{>ew ^'\el vvtf'rcu>Lj lof ^ctt^A »Vv oil P \aA\ \t 
*KacKes tUe lcue\ A* B\ The a\T m OA* i^ rjdw<\t 
^ levi^iiovi tff ovt^ cttVvto%(7V>eY^ . ket Yv»c>y< i^^rc^rvj 
^ lo^ S^cuAm < "bou-xdi iw at P u^V* H^C oi{-< ec^^- 

n< p,^ Itncc^ in O Irxoi^ Vxtv*. eoni\5>cSitA to a VfjWvvt€ 

, UT€il J Tt w;U l><. fouvtd to '^€ 'iO m<:\T€S ^Lc/ltiC* 
3* H*" vvJ\t Toe 6C tvtcWcS skev^iVcr a Iti^sion c^-f tk-r^e ^t- 



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gff\ dots v^l t..a1«ieil»j AiH^r ^.r^m-Kavidl^'sVw , w\^.cW.S 

"^"^ ' 1 what deHU,?i = "? , 4 ^'^^'^ '*'«^«-,"'^ 'f 

r W let a»Vu*T to %t VtUivv , w'ltK* J. ea»w.**3 
- t^e w<Jex to -rise iV^e'k^l^ move itw-* *? 









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wiiJi «^ V«v*%*^^r lilt levs&W c^ ^ <s5mt>i)pWctt ^ W© 4i\i«J»tsA 
"^^1^ «,^-?Wi%t^^is»»tsM^^ ^ew\A 01^ et itSft ^*j ^ft\i, Wft l^aSl'^tei; 7«AW* 

Wr<o«t c4iA«*%i* WW«*vi itie "two «Uwil%on4 'W A^ M ^ Fij. tjri 7., 

2L**Ir*V...* * '^* **** ^^ %»nt*ieit«iW«»f -re^^vcl fitc wwHeit ef 
t , ; Sfc*e4<s. <?diu«^i^ a$ q Mtt* bod«j Qa^ W(%« I3d«ie 

%g%6 %t Id^cv \cvt\ at •1,4^'sWte \ ^^mm. 

^ ^H.|?^&^t <^t«ate«« wel^h d( <*Jt" ^k«u* lUcm ^t^dl ^)Kc l<*i\}xv«- 

rit<p%^^ l^^st cgSfl linCY«fi».S€^T>rd|>«tV|0»\«llw ^^ f*^ fy<>m ^^ ^€m»¥S* 
W«^«. X«t Ike t«vv»iiti <te%A Vcflttwu** «^ Ihe fliir ^ tke i-^N^'^'*^ 

\»\6 »n fke Aam'«vMt Ore Fib d^wvtwAirtij ife wtl^l^t i^F^X ^w^> 

l| ^^ o«.Hi ^ •re[ev t» the <*ii^ fi^t N ,«»t wi«%.^ fiAsKde'e^s^l 




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5^^ ^^^ Q ^g'^HK ktyBJNo,. 70 

(il) ^>».,{ |«v€ft.fc]\ Vfi.wnsvs.a. 'WTI^e«v% *1W" AwVi«»c "h ^ )^ **^ :t<o) 

? »^ . •. ■ • 

iutwkJcd^ 1$ **«a1\edlh€ height of Iht h^yn^^eneous alm^s- 
if *s^covH|f»ipe$iiUe A**4 iri«v»^4«f)w^vi«w€ like eilti^vUeljiW dW^ 1<» 
^r^^tj^inJi Iff ^ fi.af*«Wtt 'W0iMt«4%s « »0t0l4 Iks, ^«v e*«j^ 1^^^ 






AV ■>•«« sifcsl M A * 3d.06' w. »«««;.x^5 t««j-. s^ 77,6 F«kv. 

.;ft<...(.60 ^.^^. n..-.-i feet. 



X73 10 






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^itftAU Jake Wo oKdiwt me WiIm*!^ ^ ftit'^We «mee j'^ v«fse**A 
^^X. AtSjASATIC CHANGP. POiSSdK'S iAW.-By^K 

pf ft55td»t m eic\>cm4wn m vAti A v^ertk U do*te utdvw iKt Q^i Ait *«m - 
"^ti^iKa it) e¥ ^ IW ^«.< Qyl CxyAv^i^i^^ ft^iyj^l ov reiistaince) 
v«U<ti. there t* ?2^ Imsn^J^^t/^ie;? «f ns^t' aJuj^vi TW %:is «^ 

"The e;jC^ViweirttAi "{acfs are^thoet If <* wu^ss e^ ^S sn ft cyiar^ier 

ra.t^»«<l «e^d Tension irvcreosecl Vnd>e fKei*t IKe tKa,vt^< «f ^Jolt*lMe 
•wovj^ £ttll -^eTr low Hconoflc'i JLaw * oivi^ vtce t;tvs<*^'i{ «l4ch^ 
&t \ian Ten's i©tt U «it\awedi fe e^^itn^S. ^ «x c^lmdcy awd cl-riac a. 

-b^wisKcs >tcnre nro^^^jW IhAn b^ )4AT«efte*S Law, 



f 



3^^a ADjASATic CH^^NSg VZ 

^p«v<aur€ Wii V«c)% lit!^ «t a%i» "^ AW. Cent. H\e Icn«»<p^ %Ni4ii 
Tlric ttA^O^ ^V >k|S C»«li«t4 dt4vUl4 ^ui^dtn tJi^jflinsin, ti j«^« * 

11^^ am4 tWL eo^ '^^•^Uc^iii ai(4tr smJjAfit wtik a ^tce^tnf ^« 
Vc«s«s }^e ^a> «vtjic» <x $»v%a\W v4ut«t€. 

e^ fiur^ i*tn^«%um^«i\i^n t% ©^w^ Vf\i;*»«t*x tltfcm J A^d l^C ^t^ «ri)#w- 
\avtk\ |«(4ni \Vwit -JdT cur omA ike " ]>ty|e<t J^***'* tW «»* ^iidis^W 

u.*t ^ m»^*«M^ o^ l»*f| «***4 >\fMif< »*wj i^rilfc A 

ApIabat.^ >^ _ r'^«^* ft) 

CHANGE 5 'X~-\"r"/ ' " \'" 

AfilABAT.) IT /T N*- ^ /rr-^fl. 



1u *4Pt»^r*>£flL to 5(^ its OTt^uiol 'Volume (a«^ «►*• H s>xWi^ 

Hne to coo\fta^irw %, Q^O^ Crwt- ^V«tnj? «»f %uYrtfv*i^t**^ ©Wje^^ 
?t 14 oSio^^^ to -rt^iruwf ^^UiUUnli^ ^ ^L |iV^ 'Ve^i^me^ i\e, to iV 

^W tke cotvv|prcS4»evi \^ \K& trr^t>uu v^%c5tori was ok£. «3Vi*«4. \ 
tK<?w(^€ i>i voluw^e^ tt cool^ cxAatvv % ^Q Cev^, the **v*siok 



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% l^if^^ ^XPANniN^n STFArM 7^ 

lt¥S,r^OUK^f exPAM5>mG STEAM Fok.LowmQ 

ViAR JOTTERS )-AW« Aiti^«*^k ^Ji>?5 d* ^dl Ih. «f eneral 4Udi^ 
Mft^-rio^Vs law «W 4«|>a*^mi? /WaViV-^' o^|jkl^in (vvs?^«i S)»«<Sfltl ^- 

"We ^fcjjfabed ia iHiS case fe j\Yui tKe Wdrk isv^ Jscr stroke*, 

3 Tke"Wc1<.)n<sst4,r€^ i^ caw 
* sVixnt cift-^ ^ /^^ ^ Fie- 
\^<i the «^<L4. c^ tke |ns- 
3 •' -^T- tdn <?«^^ a lK< 




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%W1 SXpAWBmC STEAM. %_ 

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Vtae Kmk^ti^ wVi^i^ii %jt Xei/A of Ike prif^e tJne W«Iy«* 
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wVijle mat tf| ilic ma^vuA*! suyrou.v>clmi^ rt»t Jet \^ - Iz'J ^ 



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ft'-\:^lj ' • •) Jjtad oj the ^mh eii^hnJer-, 

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EXQrnbk. Ut ti^ force erUrast 4 I ' ,1 

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-n <3t5 m rtie two )>y^ccdii^d § § 

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So ^X,M 
.ooH-Z 


Coarse San<i '* 


,0 n 2 i .001 s ,oost i 


j)oSo 



M.1^» ThcSf ViUi-^bf^rs cUmi«^'ih5«i % ^ j^er-'Cevtr 



-J 



levN. r^xccl iiLp i * cd- "^--a^ 



1 '\ \ V C ^Z >-*-r - A V '. ^V^ r \ 1 Vt o. ■ 



HCi'.ce i»^ T»jS. y>e.r s^ 



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SUT^' qC i- -J 'vv i:i\t'> ^OSii 



For 



ivl^C' ,' D 



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lU^: 



Coi^W^^-mf frc^f ftH»j lomi'tia «f fluid ^ Fij^ i'S'i'^ j2«« - 



Ter^Vt^t tU ftie caS4J tffa** ^- 



h^Hf 




rfft^p) 






aw4 fM«K Taii.OCC. 1SiQ0iV%0 Ci&W,{?i>HeH 






if adwtj fdwc^) ^ mass ftf latniHO. ^ w^ Vwe 

< '""** ^ Ill— »«»— I I - ii I 1 1 II t II II ————ow— —»**—■ I ■ '' " . £Z' C 



ofs* 






^u-i^ ^^oJwe-^f 






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5 ^^^2:zrrf¥-^ r 



xi/iTv^iyi. - - 1 -'^f i->- J' ^-i'- 

A'iiiW} H.|> iarres\e-n^^ "J'ert.^S {a ^6 'infinite •nuivter 4 
3 4 ^i ^n 55 J, ^ 



(s) 






§ ^70 BavRrJQULUrS THgoR. w,TH FRIC T4QN 137 

Ti.ehsiftM oi leixcjTli) o.^ *U Il,e oUier tc^^.s ate ^uc\ Oixi<S. 
since (t is n,e c^mocmt tj u>KU\i Hie Sum o^ t^e tw/cc 

/ehfia! hecui)^nae dov^n^ .treavw localJ^ Jacks of U.^ 
e<jj^a To ti.e 1>ocvr. otlb€ co.re.\,on^;n5 ^^^^S at 7/ /fe 
uf..sW€an. )6ca\.tv| or secUu^^e .>,aj caU it 

the Loss OF HPAPi ^' A, ^ i' r •»-• 

JfsjdyoMhc Mean Ru^L^^oy Hydya^lc i/ca^ ^€^4 , 
SvmV\y VySr^YiC vai^«^S of tl.e SecriDU . For a. Citcu.Uy W.bc . 

\ ^.r\-^na— i^c(- — - while -Uv ^a 

V7/. P[?OBkEMS i)vjV0VV|(vjc; FRlCTIONJ-HeAOS- 
Qrv<^ EXAMPLES OF BEK.S THEOReM vo-th FRlCTlOW 

^"^ 1. •> * ;. m ' <:>v<u;att. y 




i?^^ 



0, s: nj « -U, 



^ a^schar^es mVo tV>c avr W W >^e s^^, sec^;^! av<c< 

wafev Cft^umta ua the 6t)eH ]>i«om€l^v at n 14 li^>)e<L,Avc2) ^ Jf ,^ 
0^6 tKat Wie Wes^.VieA^ at Tl 'is > t ^ '^'^ 

oo^ Tl-ie Uvtjtk erf Y'^^ f^€»*^ ?V""t, -hi ' /s =^ I . 



•V ¥f«om«« Vnown^ Oivni ^ ^j , .'Hb«j The vekc - 

^rfu^ UnlJ^n^ eiY<uial^ SfCi^^^ ^f <'ii'^5m^sr f£ Ttduct5 *4 

The )>jJ^ Cm ^^'^ ^^^ '^^- Ht ^ '^33 ^^ ** V-r/^X 

<^ir^lUf 4X^ The It^lh ^ ^^d fhe 5fH^re ^^ /ke VtU^f^ 

^^ffui^^yd y« FW*!^ C'il) Jh«H.w^- iari«C farli«$ |-^'^:>c- 

i»€*H«^ «^^-.W«50^'^efo hesY^^t ^i "H iS «|i<al t« five U^l 

S ?H. , V ir /a^/ fett t^-*Ht<^ 0«: <5,/f^C c^kf i, [^c^- 






<et.^^V^<^ X:z ^^'^ jt (n Urn}. TvoK^- ^^,(1)^^^ 



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i>»e lo^jciie <5N The rt^^^*! 



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5 






tX^^h^t. If *^e rtjsWe Hue force Cr i'«^ Hvii )»Ytfk- 
©f ^ 4Wwi "fsVe ^vt^m^ jW«. r^<^^ hr^at mc ^orc^oinj 01^ <x. 



l»« 'V 



:an<i ft.6 ^.^«l»w^«rea c4 7X >=■ f; = 7S *t' '" ' *« ^;-''* 
1.4 "K = «« ft.,«via tiie ^iw«v;sian3 *i ihe >»•»« «s 

iJitsniy t0jo »^_ : _ •— ttTTTX 





"^71. loss OfVIFAC W 0K\f]C2S AN^ SH^J?T 
pipes. 5o W^ as lV»e sl^^Af f^^ \>erwe«rv Two VoJlhis 

"Wnas OY dWowS^ "rtse '"loss of "Kea^ i« ^swV^ci s^lefjj U^ 

i^e ot\)o,rc rvK^'iwr^ti (chares ,5cca6?ovA5 eadwrn^ ^v^ cok- 
se<^uewi mr<^nal -{'n«V.^n Ani li eat ^ tKert^ <:c<.u.&tvi^ o»i- 



«*^ 






^m Ihc ^Alojy jf live fr?mi of a •fnVnon*'K«<:Mi m «^1c>ij' 




-a^^rseAon., This v^^^J^ V h &\l^^ ckn u^^ievujww 




i\l( 4or a.^\ven [fl-U^.^.^ ^as*M^ 



'^75. HE)GHTS or RrSlSTAWCe^(oH XOSSg-S OF 










k 



Iftibe llevice Ihe <jY^al w1il/Uj £r[lhe conce}>bon '"Jo^^^f 
K «i "^owq >i}>€ issues JTon^ tilt' yianf Side tff 






^4 ^(-see Fiq. ^'^'9^ ^C ski^l need an ^>:\^r€SSH:>vx jcY Wi^ 









' VoA (»ia ^j>i^m5 'B^'S lWorem^,Tlie loss tff Hea<j at 
' E vJ?. C \3l3 ^''-^ ^"^ i^^^ ^^^ ^me ots if efjiMX 

: c<x^^ we sWm^ Vave ^ ,27 ^ > 

'VITe ttieref^e a|))>l^ 'B's Ikcorew^ Td fee <!a5e^ ^Ikoieor- 
tvcUs See Figs. S'^8 And 6'6'ft ^ m oracr lb deleV^tw^? 

. ^1 a5 dia)ui>i- level jor p<>levi -^^^-^l hetxaoj 






^ 5 



k 



4p<2, wh<5St value we 5si^i< . Sutsj'jlw-N^ fdr tli^ f^ '!!^ '') 
is v-aVe 6^A fwv^ ^<7v fO^vir^ h.i?».s;e -^5 ^? 

^5 ^ d-\^\ -C?-5 

HftMce vun^vo or^ fa (i^g. The bip-e i^ \ u the T€$^rv<^,v 

%-f>-< - rhiS)'- !="■""■ -^^y-i"' 

"Ic^ble ^ ^^7) ^"'^ «c?vv-.p'vtte the follDwivn *i^Ju.e5 ^s^j* ^ ^ 

trance if{ ol ]?»J>e ^ Coyntys not "HjuH^ei ; J 5€C Fu>, 5'5'f 

f<^o(=. fo^ g-0° ^f^" 60° 50' -^O* S0° 
'^= .6'OV .6'66' .635' .7/3 JW .S70 ,?37 
€<j,C^3 we see H^at" ike )ci>S <?f>i€A4 dft Hie enWcie 



"TfO Wi 



I| As eoYneTTS at £ are ]>ro|>«irlu TOui^e^^lKe tyftrafncc 
less erf \\€4:td -vm^ ^jTTat^tea^W l?e cl^nie avA/oj^ witn 5 s^ilt 

^7^. GENKRAX form Op B&RNCUXUf'S 



%4-7^ ko5Se3 OFHBAD (^y Q£W£KA,., /^, 



^ JL ^ ex:<:e^t skivtyrvvctiovT.VcQ.c) for \o«A^' J5i\>?5> vi':^, ^i^'—i 
■iVie "U m ec^cVi co-Se WwvQ i^Ke veloc^tc, ^ '^<»^ew'A «9y KvxKwoiA^vv^ t/L 

is Hot 'H^Cfi.^SctlWv «.(iu.cvl If, nj or Oj r\ 

OF vv'ATE(^ .'N P\P£S. See ecj.O^ %'t^^?. ^;c^?->('.vi<^v-^^'5 h^-e 
"been vvia^e \'-f VVej.jtj^c.V ^ £ ^l-e'\ w£ui. ^ T)a.r<H»j f3oS?u.t ^ Pyonv/ ^ 

LA\fVJ I. That f <i£C->dCi5e.s vulTfi.v% U-ie velo^^t-. ■.•.'xCYectSe.,=t 

-fsiet l^f-^v 5eC. c*-^,d '^ — s2-r;:>i> "■ v='<^ 

vv'hllt -? ■•' r: OQoU lit. ^ ^ "■ P.'l-e 

LAW 7 . That(a* <V liie cci.':^e ©i s\!i:^?vig 4'/(c"ijc:^i b^T'Aieev-L S6hc<:>) 

wWAe. 13a.YC^ jA.k^ft ui(o ixccvt^vvxt TooTW '^'^vu \ *».0 Law il 
V^5 s,.. (see >.$'85' K^v-.>u.,d's CLp|jlre<y y^^echi^vt/cs) 



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j'^yy-q^ COeF^'(C{ BN r f FOR SKUv J-FRlCrtQ N /^ 7 

"'•■ '»--ff.-' ^•^^^"^"■V /8Xd,.«..ftJ 

te^sioii UMe (;>f3. I^t tc ^^6 of H,a lock Y^cyy^J U a1.coA 
v«-Ve^ erf j -for ckon (Von ;^.;/?e ,crj «lUw,s. fvowu '^ .V.t« 76 ^,,^ 
Qvv3 "for ve)o^\r<es of 0.| -ft. % ;^0 fi. )>evs^c. Ckf ^^tS iKg. Vc<- 

The Y«com<^^ev^da,tu)v^5 ef h/\r. f'an^iV^cj- Se<v^^ ^D ji-is\<fw Hie foMou.'- 

3 x. ft j^-i 

Fdv ^Ui^ViU«| timber ^ibes er] 45av«^5. r- y 1^ • ^^ -^ ' "^ 

w^ l^^cj^ aici ■ 53% ?^^% /^% /3/o; 
W€ shcuX^ cU 72 V 6o /; 38% 2^' % 



<st line -^- C>i ^AvKnC'xQS Kllfi -for 4<an y?^^5 , ^* 'tt^Of . 





covis^cUv^cl, The vdo<:;u^..K,^a at Ti ,v...^ ^^^ 'b^l; ^_ (3 ."^ ^^^ j,t 
clowv^^ sfTe^vv". section ^i'$ at ^ 'K^'m^v level 1\-xo,^ ^l 



/^c? 



<^j 



U$t^ H^ fi»,^U, AH^ See,, w* kowe |j« Xyc ji,^ H»s _^ <5.^t3 -fir 



4\S' 



n 






0,30^38.6-^750 =:: iltiro-. ^i JfX£iia.v^'^')' r^l 

VST ^/<t" ['^v «««. c^na d:= %f^-,^Vi€ ^*^Me> I2#6^ ^;^«s Jc.oo^e^ 
Pipe , .•v.cWi^ %«ik ^vun,,n.^e«.a ^^ mhsmet Ui ^ h^3 

(^«»vtieys.v»dt YevL^ded), Rese^vetV Uv^. T*^. J'^©, TK^ .jet iS- 

^^$M*VTca Tft hi^ vi^^^Vm^- full, ^ua U .MKe v^i^<.C^% ^.. ^^^d 

^c^ ^•^%^o'^0'\■'h^\^%..^.^^il.vJ 
v^sr ^ '{jcv Wit of time «H <^ y<j?€ of Glv^vu Uwi^Tn I ahc^ <^5a*v,, 

% - ^Sx^S' If ^^ ^o<^ (,^^ I ^?33,wK:I€ f »Hav i-^€ l.J.<^ f..m 
veWtC^, .f tHe H- ^^ l?i5i^ J Jf not «W 5ee ^lot. ^. sx,^ /f,. 






|€^fi*.^«t M ^^^•^;'^ yfyjo^ V5 cose, Sm<e tt,e j^t WTKe s'^-.< 
of e^Jox . Siuce "5 ft C-^l ^ d^^luds on tKe «<iikvt.c»vvA «u ^,5 '--^sK 

i^in ^^f V^ ^ "tk^vw t"e^ki?, «c CorV<5^evv2m& valine for -f «ivic^ soi^f .'^ft/i, 

o\«r«;vic;4 V*"*^ 1^^ -fwjt ^^tx. ''^)^< fT^ 4- Ah4 Vnus CK 5l0{ <lo3«iv val- 
ue itiy «1 i5 <3SYiv^<i ^ «»'n^ d*^ ^^ "3t^i I \i <^^^e lav^e VA/e rv^c^^ yS 
J - D f*^ ^^'^ -t^Tst tA^\,ftiii"^'v.i^ion. S?$ Vst •f<;<5u,Ye -for Hiese exarvij))«S 

ft^ (~ *?£ i!!? ) is lost Oik tVit -tvifvcH^ce ^ C^ c 90^ ) ^.kcI- lo.^i 



I 



^'fU- 



EP(.AMPKB5 Uc)N<S Pipe 



/60 



B^cainJiJe H, QVc^\<^■{rox^^ W«;5\>^i.K3 Re^^-ii-^d Uie M'yyjey^ ^Qi ^ 



Xfr: 



^yox^'Vht UUe ^¥*?^,-^ftV -U- €.0. f^^«< sec. oivto* cl:r i?.'n. we 



I +. 






(J^c: y^ of <* <t<Wc foot cr( wo^fcv \)ev S<C. ueAcUv f> \i. \\t.CA.dL(^\) r 



4r yjV/<,<5a6Xi'5^ 



if. ^ 



lO ic<^< 



^^^ 7r;<..o? wW<cV_sJ5.6 ;t..,c.^a-u:r7, jr;.Ci)60? 



^ ^76 



CHEZ>r^6 FOP.MUl^/\ 



/6 I 



v.^ AouU •K<xye <^i ;^ :r |/^lf ^ ^V.\e ^+ '^c f«^ 5^-^v c Corn- 
ers =r i.S06* oH\vi, ^ ^ 









3.0 

/3. 
/6. 






Xo 
16 









Jo ' >dY Se<,^ 



¥77, BHHNOUUUrs THECK^M as an e^XpRBSSIOM 



n- 






% ^77 CoNSeRVATforV op H*MERCY ^^\ 



'VCtt.cUiM^ )oweY <^i-,<) )oWft-^ levOs, w.lKowi amu covMfxKS^TiKo 

$\ft|5!. )Ka,t TKe stock o| enerj^ of a. ^t««.H. J3a.Ytic1e , <3r St^-vo.tl 

<JL we "Kctk^tiixe oi iVijrdl ktw^ of e^ergw w^Uk Vwa>4 le 
ca^\*a PR&SSORe-ENSRC-iY,ov ca;},^.!;. for ^oU^ wor^i by 
virtue *f «Kr«>»val f\u^ pir^SSWve ', 0,5 \>^o^^ l.<^Us «xj>)am<;; 

In r.j. 6'6l l^ wafer , v/,ii,. av«V|j sUvu b^oto^t c^-^<^ «<k- 
- V ^" ^^ -^ "y^/^i:^!! ["v^ Jj^:x ^«^^.;^u<t j?^^^**^ o. )»»5Vovi the sjwice 

rz::7-r>^'i^^ p --— ^--'^ be-jo^.a wHW-k /s ^/•itcu.cct-s. 



tut off e«a tKe Uft fir? rv,t V'^"«H Av-.d 6|>*^v»ed ovi ^V<e >ti^"ht:, wKi]4. 
tV\c w<^r«.Y r*v Hit. £mKv-.<^?v -,^mo ^v. Hit kft of H^fc Vj&tcn 15 )>t<C 

va. "^r. ^oYCC X ^'«^*^'*^'^ = Fl>X^ = '^^^^ 
a. va\iMvi€ of v^a.rcv 'Vn Fs, weCc^XjHj Fsk QU, or oIK^lv 
*^»0 ^"^^"^ ^een u.*»eA^ A.via ^i»^ {^^ssivva 1hr<k"' H\e» >ndtorj W$ 
ejc\>eYi*v<c«cl vn© aJ,(>T€claJ5!^ tUawje Im. veloc\t*| A^oIiVh slow) 

a?? /As pressure, 

Kow "W^lde work otTamfid ^IJ ^^e Cev^sui-wlpTteta o^ a >A/ei(|ht 

W"=. Fi,s= Fsf,=:Tp = T^i. = QA <0 






*ff« irjAivj now s\^le ^e>tTou.l\I*i TVieorevw w'Adu.h '{'5^«^»«n i«4«i 
•rt^sw jeyw ^vi-j»', Ktilt;ylt^ €<i£k term fc'l eo, 1 ^% ^5'! W l||' 

"thtt Vol. ^ ^b m, di^&.l9i ^^e i: |.rf*scc^e id tn ; v^tfi^k ^j/-! 

!kw.s *re&a : The a^^TC^ai-h <km^unt of e^iar^^ (a/ fte 

ettef- ^€tff^oW as *nj //x s/e^^^ ^7^u; coJfhcut frtef/^n ,'^\xid\f 
Ike sWe <ff €>,ey6iu \$ conetani. 






l^fiK IsT^^ ^^}\ C«^^. .^V ^^^ 1^ ^'"'^ ^^ sk,v^.^fW«r.fln r^. *>v 



•jorm cr| neat ^«vxer<at1e<^ U/ the fvictioii «( tht Mt^uuifi Wvti^fes 
flt^Aivtsl cuxcK a1V>ev or tl^e Sides eij the 1a'«()eS*> 

^iv^**sv*tm a4 tv> tHe>/»^ <ai. the ih^cyh^I '^ri.ti^vt yjS\\\ We e-f KSg 

.S^^ il»e sec- ^ t?*«Al «i1rfLt< U 1'Sc SatW^ ^&r I90IU A av^a S AtiJ 




H \j 



«mJ in tH. ^•sfitK A Au^ B^ftfv 1^' ='§ < ^^^^(ctvcti 6<^w«.1 losses J^ 
W» of km<^'i^ «KCy^c^ tH B ^i Wat ^fit^\^L%^fM. jor \>u oivi d- 

<JU.W\ GAP* ^ ^Tt$«CiVe-€wtVf|Jj(A* it i& l*r A3^ ^^ *J»t=«r^**^^- 

Vaftd (>r^ ok ^ \k 'B ^louldL b^ 1^5* %A\x %d (i^ii ^ 



§^7^ kOSSES OF SMERCY _J^ 



^uuUcn CMUr^<tr.€tTt;lWe watcT <o)".w,n oi TT? "m B iS f*ur.<? t; be 
ot a less '^e.\c{\^i iKcn iWat ett m V«^ A^wK^yCaS c* n f^e^ arc c<^«*JL 

>T?5«u\e^«ncr^M.v/*A »c c^iA^^c erf )>«t€*^T^al encv^y ,1*^1 >n "B ^ 

»u:(^rred \>v^ Die vft\, Q. 5^ lic^ulcl . TKe value 6-f 'S JH. ^5 

^nc^ien^tke C4YW6U.V.1 flff cacVi Us.$ |ftr ^x ^jven ^^•e^^'Kt^Q >4 ''*''^'* 

yx^t T>e Q,?"^eu..*{t cv| tlie losses ©f "WcoLci^ov V£^<^Vits «f r€- 

^\sVar\c€^ due I'o the%£ vc^VtoviS c^^usts w^l viawVe conl.'i<^«Y«<^ 

y CO- e//! «( e>>;t <^ r e s ^ s ^a^? r e ^ in €a«V> ca.S € . T k ^ v e) e « •. t^ %) 

or^ Ft-€\iee-»g jScocenWj Tvas V>€ev% 6v^€; ^ VKc I'vtest Viat«cl €ixj>eri -■ 

^7<?. L6S^ Of HEAD "OMB To SooPBrv (ue.S^U/^R? ~ 
Ht)<3BX^)?NLARC^l^NlENT. BORX)A'*S FORN^Ut^ .f.'^ 6\43 
, --y A^ ^^4.«j Is "foY'vie^ Ivt, the AKgle wMix c<n^. 

U Cg<y'^;*;^/':^F Seftu.*v^4: less &{ enev^v. S'm^e e<\<Vi V**r» 

F«g. 563, cjoCtHst the "^Ase <K me lU^xWiUW t^^-^at 

c«v^<i tHGV^ Si<jvv/*iij tvxov"rr\<> coluiA^v^ cf w&Pc'r ^*K. Vri€ ^a^tJC V't^C^ 



a*\c( of ley rtift iivjiact ^vvoves 6K w'ltV TK< SAvm« ueloc'ity V , 
Cis rti^xt c«liAhan^ jtAst as JCCUV5 iVv inelastic, d/r^ct Cc^Tm! 
r'rn/>CLet(b6c) ^ l^^ ^v^o^y f Ik3 tV.e evs^rjij last locj Hi^s )»ATni'. 

^if^Y oveai: Isditj cr( watev UX^^ Uv^e >»i^e^So lV»a.t M - <» 
Since F; ^'^ :r F^oj^ ,^^^ l,e vW,1tev^ 






I 



r. ^-^ j\ ^-^- TV,e vesU^r^Je S€cTf;%,d.l avtcis o^^ >^€ f^<s 

H0T£, Prc.aic41y The 'flov^; c^Knot a]%vAt|£ t^ iv,a,k/Ai^^ 

y*^t t^:ie ''v^.tciHal ]5^os^>< eft F; ovv^d *tt zero oy Tje^ctTj'ue lU 
assuv^sV^CH is ivvco?y€<t.. TKiiit \5 uvt)e5s there is> somi ^.r^^^Sttr^ 
at F, TKe wo^Vev w\n y^«t Sw^n cut We>cOW T« {hi H>elax^e Kijje 

^:^^^^^M^^^e CKlij loss (r( Vieod Cchsicl^y^d iS iyoL 
n ^^ f F^ -, d'^e to me Sc<a<i<w eOare^ew^ev^t Csk(v^. 

lUe v^^crveW ewtvPiKcd Hos toclyiS^J Corners^ At^i»^*j'^<f ^''s 
^eoevvL § ^7^ % yY\ A.5 dov\*n*ilr€4»M. s^eT<oK,A«^ Ti rW 

weK^ve ;<4.1+Q_ c+i+'K- "^ ^/ C<i) 



T<? 



5U0DE-N HNt-A«<Jt>rtENT 



n'f 



=r ^/, ^V f^.J»«r iecC*"^^ -faJov- O.0*fS' vwC^^i l< ectlU^ o^ co- 
efttVifci^t of ve'lftMrw |6v tHs's c.CL$e^ Ttie velu^^t d-f -(low Jacy 3<r<oka 

twi:cn) i, *^ >1 ^ ^ 4 1? -t "K - O ^ - - ^ - -(>,) 



A /G 



.^ X 



ifSO. ^HOKT 9\P'e, S(^DAKt-HD<3)^0 JNTERWAV-Wy. TVs 
1, jvovv* tVvC Cfeift'bac.te^il ^ect»on ed rh'j/XVtos* 



K .'•'Air 



^^TS5^^ 






%if8o SHORT Plpg. TWn-PWKAgM IK ftPf . fS9 

tvAcUiK S VS7}. It ^5 >voU*Uj torr»e^\,dl larger ^<xw.n«^, 

we 17«<^^ S^j^V/ Ut«t KyvUsS K U U*S "t^r^axx ocVctd Vo «fe<t H,e 
If HiC ^fW Uk<S y\^<€ iK^o ci.)»*^vtiQ3 va<:cacm Hiti limiGK* vc^. 

Tilt <ti4|AvA5*K ^i*^ \k •'H>,;l^d*e^ ]i.t H,^ c\Y<»^Ur 4<vv,;^(^ 

F :^ CF <A<.\>CK.ot* 6K F "but S«u<e eic\>«»»W<Hb ax v\^<tsiayu 

Hyfif^:^ .10 .2.0 ,30 .ifo ,60 .60 ,'70 ,^0 ^0 i,06 
% =: a«6. V9, aS' 7.6 3.7 /.8 .9 .3 ,06 0.00 



1 j^fe^ 6ooQ£n otMiNarioM Of s^cT(oNi ^6"? 

^W.. SOPO^N) DININOTJON Op C floss - SE»cT(oM, S^OAf^ 
I Svk^d<H fenlaYfirC^eht -fYftrv t^ie Coy. 

VWtloS* M ^'><<>'<^,^^ Bodas -jftTtMOo.^ '{^-'^'"^-[^i "l^'^ 

^Kencea W<^ }1h e vo.\<6 *{ f^ td p H^t SccTtoWal ft.T<5a of ttve 
Ikfl^ ^1*^^ >'>c.tf.Wc€.>] »j ~ D, rcv'o\Si<y values «»f tU^s ><xTtc 



r^r - 



fi'Po=^ *'^ *^'^ ^'^ -"^ -^'^ ^^^ •'?*^ ^&o ,90 /.oo 
C - >6i?v .fc3 ^ ,(i*f3 .S6-^ .^%! .7(1 nss .%;3 .$^Ji /.oo 

C \>^\n<j •(oi-.n^ Vn' < cow.Vutc '^^ -fvont ^. C^ ) -for uJ<? ^k €9.(1) 
^fS. ELBOWS. Th^. iKtkrna\ dC^WyWaiice cotusec) \>^^ a*i 



itra.^ t^6° Vo" 60** 8o*» ?o" /oo^ U c '^ lao** ISo" /Vo** 
'S -.0^6 .13? J6V ,7Vo .^SV /^56 ;.6-6'6 ;,8«i^ ^^6 ^f.^j 

% would ^V6VaV>lw "Vc iorvt^ wVifli Swt<^.Mev. 

V«A^ H Hot Wvar«Yioa\*j Vn<Yea^e<ij 5\Vce ^Ke e4<iij iVft te^^^s )>i^€ 



§^^3 



^kBOVviS ANO BBMDS 



.' y^O 



ut 4T01 ?H, n>e i*n,€ Vatic, T^^' hiicci ' |i:^b^ 







ASS 



<rf ^^a3 



^' ^i n to tKoct of ti,e first ^ ti,e toj-c,! 

U I '/:i times 1Kc«;t of ©tie a\ohC . C^^isVoick} 



^'o\ t^' Ra. 6*72,^ \\xQ ^^ixlcoS. forh^<^W «for '5 , tHe<o- 

<icWr\«neHr$ oih3> 4ovk« &{ 13^ P**'^^^ yil . 



rtU 4^vvi<riroo<i Hi^i 1ke )»^vU*u -BC of t^e y»^e Is kc^: 

4Ua5\ Wet tvte t***^» tvWick *no*»»tv«v- ^-nAjij H&t tec )>va.«.ti<««A»l € vw- 
"l<.$i BC U H^oyeTlh^4i i^^« *ir fouv t^mes as lo»\g <\s <v;4<: 

SittH$ oV^o'aI lWe ^at-n^ loS5 of li<A^ c^,^ <^ ^t^A-slvant "b^nd^ 

SA««^e >W«c,F{<^, ^73^ o^ficsta*/^ c^cUt<.U< )o^s . Bm ^v^^ 

a. 

T^«^^^ .10 a-lo ,3^ .ff'C .6*0 ,60 .70 .$-6 .^0 ),0 

% = J31 JSS- jSt .!lo$ .a?^ J^^o .^M ^77 t.^o L9^ 
¥8^. VAi-V^-^ GATES m CYk^fMDRKAV P\P« 




fi: 



,.. ,^. ' -f 






■J 




3 ^ VAWVt 






Vdv€.^<at?e I Tj^^ ^?€ mW 







W hAK 












F,^. $-?4 



X—" 









^aU«vi 



<«• 7SV. 






.^ 



fvor>» "Bernout^^S Theorem ^ % V74«^ we ^ave (^t^ = ia^uty^^^tvtHj 

^ ^) ^3 <!^^ 1^^? ^^j 

rvof^S^^S^tc.Ug 4or c>i^<jo\^^'UcxKie ..'^5= <5,6'CS' 

V 1 ^n for scua^v. <^.K.,^^u, ^-b^ s;,^ ';^,^ 

'^^^^ ao32SX7.3^6^rr |7.0<^ U^t^ Ah5. 

i%t ^(:\s ^6 s»>.o.u (y^zz t.^^ ft-^v sec.) o»v*<a iv«d i'k, 5<»,<*^i 

lo5*<.^ ^ 'h«.ftd a<^,ev^d 6V, tlie . S^u.o,Y^ o-f W^c velocity (h^arly) 
>eserv6i-r ivi \t^Of» 

£^Ani^/e J^. Tf^. 6*?7. "^^flt ffi€ v^lve.^afeT Wf ava^,(x 
*^C«'^- 5c-i-<;i U F^q. 6'7^) ^«<i'**-'^*'*^'^^^ vo\uvr.c <i«lt^^<iv~ 

<4 >«.v 5«Cow^c> tVvrc' ttie >;|»C ih^re S Wcwv-i . TK^ 3 ^^ (S^ 



I 



§ V6S' aXAMPUES. LOSSES or HEAD 



/63 



r>%4<vi- 



SeX ^irh .Sft*ar« corners K^xVnt ^^A <yfUe Iay^jc o^>C . Dti 






R> 577 ^-^ -^r-y-^.i-... i.e lost »( Vic. 



<*IV 















18-3 






^*6 TIME orewpTVlMC, VBRrtCAi. PRtSMftrrc vts- 
5EkS C'-R INLfelhil^ PRISMS iPSo-rroM is Hoft.:i6K<r/^0)ON- 

Y^vAR,A8.6 ,^£^0. Case Z. Th„.jk o., ,.;^„/„, 



sViovt K.t)e VhIH* t.-m 




«ilotva 



<i==^Fj^, ^,_^ 



^tl* 



^ti^i^'^ &.5 -fev^ ^ 



F>-e<n^ \!)w< "K^ue 






§ ^S-6- 



"TlfWVF OF 8MPTViMC VE^S^VS 



Ife 



>v^-^e^^cc V>m ]iUJV»-v\A 2: ^0, ^^ \(k\j p tin?. tM^*-!^ v>ec«isa.N 






vv.< 



ET -. 









^A.t 'is ,T; ei-k-jDn^ TVie. vessel nre^v^^^s ^^jtcl/e Tl->,& ffme *r{ c^i'i 

To //?/ -^M^ SO*,v>£ V 



si\rvt<? -ajvtoc/wm'C oj x^4.\£v 'ij V»e v«ss€l Va^ ^«n 









H5A0 VuATS 



* 



~ — Fv' 



iL 



Fv^.i)?? 






■,Ai)-.vv,^-r$.fv "^ 






in 



boiUti-, w^osa COv^.{f c.'ev^l of effW^f tvVv^iVs ^t^'\\v^ a>eK \6 kv^ovA^n 



G f f 



i?o s^. ft. J wKvU 2 

^ry\^\y^c/ J ^" ~: — — : 



^^roy^ ^^..(^'3 (ft. )\». sec,) 












: ^^ A p 



:v 



(?ffi;<K ^r.k,;y ->U.<i 'tK^,' ^ ,,^;^^ ^^, 

*i F* fi^Hd F" A-K* H^^» VoV^ronral ser- 



:?:^r^T-tT- 



t<inS «bf ttr€ two ^vii<nal«C vessels (ctyes vetlrco^l^ w« W<. FxcrFy 



■'•''= --I'+fr.] 



^ ff^ f TWO COMMUN^IC ATttvJC VE^SSEUS U6 
7;«m€ /or Tlrt -^4/ W? V - cilX , o '^^'- ' (6) 




L'' l^te w^tcy •st<Kvv<is <^t 
a. Uv.«:1 MM = m^ c{ tc^a 

^rlsmalvc locks. k*t ^t^ 
\rcrvy rK* 'Ye^atoi;t Vol. T''^ - vol. F" K^ 3 o^^6 \S\e. ITv*;^ 

^•"■f ">•■•••■*. =;J^/^'--r>j <«■) 

As ^ooh AS O js Su\>mA'r<5«cV^^f f I'-^f 1<3^l*-«-S P'««.Ce t<Vi^<V 
Q. 1recTb^w<)u.Wr"KoW;Kt. TV^fi -Stae^ CV- «»verf ^M . F^'^.6'^Z 






%¥%6 



TIMP OF EMPTVljoc-, VESSELS 







2 /-^i"5~ 



= c\t. 



*^new?£ 



L '--^A^^^^J.^ -=-v^;?,rz^ >y^K'^J 






e ''\*vU ' — r"'^';vr f sfvj<s 4 



.L. 



vov»^ <i. t^^^kkv 



I -A-'e iv^cjfA-t-rtf tv>^ fsivi? 



t^ jor%t '^*^«y ''^^ 5«Uk to tKe ^«-- <:/f/26 s^'l sf lite lishk 

hot owU. 4a<s nit. v^i^^octtL 



>a Z^=«rc, 



>- -'^u.^'X v^^^ tVoi ^,- 

oih^ <^V6wS less , wUe^ccLS .-- ^A.3<i r c^K.d H 11,e -^r^f 



«c^ of 



i -^^rst, >e;r :<s^::.!:e 



icjt lloYiZa^/acl «tva UKC/4V/-7 



Cas€ J". Tu^^t^skctfye.^ vessel ^ 




S4 



rke 



c>;j,<e^,lr^ Th^ ed^C^i^ 






•6 v^Wijj'y 

wUcU vessel 



% V^6a T.A^ c^f EMprr.^ GF.f^- Sci,:DS /^^ 

^ ■■ La 4 1 ^i. . _ /^ •>■ rt 






F>,/W .- (s.«.,.fo3 i=. ::il^^^ ^.,u„.. 



*- I — ■ I 

■5 



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V 






^L^/^-z_^^],wk;!. 



- ii •^w, 



Wi Vd 



I. 



v<sjj:*i the <'>•£- ^ Si 




^♦1 Jr<i/ r-^Te o-fc'usclt 






V 






^^S7 TiM^To SKKprx iNiyFiereo OB^U^'M ^6? 



analo'i^ H >\^H«$ a^vidl w'tfU Sides 'r€S^«t\%^eTy W^tht »0»&^s 

Oub N(^. We Wavtc maw suVdwt^«c^ 




cW^.v^j <,wa of VK*2yiJ>e^I^ sc^tU ',> u.v«^ /,$ ,V the j>}<i(,^ .^i ^/,^ 
"^i«ii<. tfc cwvIjTy Tke Two v^,«<!l^<s s 3 

|\= 60 ft, 1,^ .= ,0 ft ,1,= ao H., <^.J ^4rk of waT«v\, Uf< 



I 



^^%1 TIMf OF gMfiTYlNiC? T^^r SET? VQ|1?S 



f70 



And ottc„'vt yu. -^s: (« ! T ~ ( *— ^ 







_— — <L--r^i ^zM....<o 



wVerd S IS TV^€ vt^Yi^Ue a.Y<CL of Hie free "^ sc<r'{ace ^t^ny 

Ivt TvA. S'S'^, ^Ui<.k -^UowS CL "}»ow\«l *vlioSe IsaTtoivt ^Asl>«H <jc * 
CuYCiTftlY Su.Yv<<jed<- So TUa.t w< Uvvovo tKe va.)u.e a-f ^ fdV^KU^ 



^^%% TIME OF EMPTYING PO^)D 




nf 






.o 



of tKe Yiy^ '** ^*5' ^^'^ C"*" 
^o «»K^ f>«f>»6 slio rt oi Hi 0.0 

:-^^ Ta>nce jror^ O to H (.^ ,»^ 



^•^n o.^ ^^^ Tine o. j^r^V") <. c| fe^tr? ^«^^ ^y\ i\axtiV< Voa«( G'f i: - /6 ^^' 
so tKctt Itxft scv<M^. vaIh^ o-f yu. =r , 3 6/ i^c^^ Ije u.sc<i V "Let z --? 

S.= 3Z0000 3,.ft3 S^= a^o-oos^.ft.j.^S^ Jo..o' 
S^= .So.oo .. .. ,uv.u ,.= ^ , ^. .361, L^ n,e J, 



^1; 



^ i^VVooo s«,. 






t- ^ -»- . — -— )- w 

'^V^'^''"'^i,v-^^^'%''^'^" K'-'-iy ^^*n )..w».„t.)Am;.a Axe, ^ 

[Vol.- '^-^ 



3XV 



= 2j 1 60,000 tut.ff.J 



M1ME.P BY oeset^ViNCi pKoCf^gSS OF ^MPTYll>/R.Tvx>«»- 



^^%? 



VOLuMe OF l«r?i?CUi:AR RESERvoiR 



nz 



^orrv^xvt^ e^,Q^) ^/^^^ ^^ ^^ve S dz. = -,yuFV5^ Z ^^c?^^ 
But Sdz IS tlie u^'f.^1l^<:)y s.vall volume c^V of wc^rey lost ty 

^1 









I K<S Cqk L 



•CO 




v. Vo *3,V 



*0\> ij 



Ruc)€ 



su. 
Vol. 






o VCH titcw»V5<-v o^ sc^uaI l^a-rS 



^A a^'^ • **f '^^ ^eacf of wo. 



/?l5r^_5i5 ^i U^i^*^^ o^<^t4 v.vi,<:^i h<;<j\t> The ccvJr^$}„^^,;J, 



H (se< f('^. 6-^7) 



»"-1:A} 



+ 



5z %.z 






..tt) 



^9-0, IVOMHrN'CXATURf . F<j. 6*S:gr, lvV^<v^ w^W f lows 

^w6 >;^»cl^ \\^t t-.[))?<y -Surface f's 
'5ree Tt c6v,fc.Y\v\ »vv sliu^^e t<j rtie 
dynamic «ona«l«cm5 of c^^*^ case^ 
vvViUV *\ rc^ulare to tl?^t €-xrenC 
il\e sWa}>d of ^e <:vess iecTton . 
Intlie. vtrlical Ivctnsvcvse scJiciu AC »Vx f^-^uv^^ll-xe Yme AC 

civiA $tYtt.c^'Kt")tvK«\e "^le Ime ABC, a r- ^> of tie «r[ihe l>e4orMc^ 

— . , / - : -a 




^ ^^Q OPBN ZHANNSl^S 



73 



! -fhe yotXi'd frf 1Ke 



< "5 .varies wjrt-, ^nft jor^x^ «f ^^e iVov^4ve>ie iect»«»i , ^ 



'•never 




Vioy^^oxxIaI ana fKe ^Tnt H Q aWk^ tf-xe ^•Tto^w >$ W^t 'h«;<s>^rAY 
"^Yi^mJ'^the ,3)o^e of t^e \><G* <:>e<i hot Vj<c<sse,.riU x Sr^-»<^t vf suyf<ic< 

Surf0L(C{kotS^ aye S♦v^<^l^o.ns,o-ry.€^« «r( we^d, ^t^.^Sft c^Ur^ 
ea ou.d wti^-red as te V»e YeadCl^ seen , c^^a stAi U<.t )me a.iU<rU 
-be, H,€ v^Jnd: < Kcie arc ea)owva ro float w,tU U-^e £uv>-€^t U <4";^f<V- 

a;sT<.ViCe dtscy\\.e<^ UtKAse<^ ^c.y^^)^\ tv«,KSwet$C o.i.^,Mv.^nU(o>, 

c.v,d,r;oH erf Si.r|ace,cv.e V^U^ Qic 6nx<v l^<Wsev -^.a^ w^^T^r *vc 



ev Va>l 







§V9( 






17^ 



M^tx'^KVU n> 'flo4, u,i5Y^l,f villi Ue U»> *ju5t »ris,Me. Its otser<r- 
of <>X[ Tix^ fOUu^eyvHr It^t'^xy WcUecH tWe cw^s erf tl^e rodl, 

te ft»e <UYr<Ht,i,vli^ck causes ?fc r^volue ^.t ^ 4 *^o* near^ 

-25j ]3Y*)3 6>TroV^) % /Tie veUoil^ 
C ^ e|* the wo-reh Jj^istv.^ f{ 




e«. 



Oy 






IVtA'Kh S 



omejer 



ne >H- 



d^cat.cCvs of AK.J 6K^ »W5r^Hvw^wt ., ,\e. to f\UdL rti€. v<:iociU. c 

>cr of v^volutto^S J>er m'mccre. 

Pilots '7"'*.f.^^r;». Co\ts\s/$ iH )>Y«vt<v}v)€ of c v<Ytical Itlt^ 

^cl, fTie wrattv iV Vie TowU r<^ ^ 
^•^A^jv^s ^h>y\o^iaYij vvltti it's fv'^e 




t l*fi CuR^BNT-MtTERS UA' 






^ckCU* t4<.V< 1 WT* <:oKy<v..i€vCt Ha^«> \»^ tine ^«««t t^f l^^lvvM^ 



I 



'^ =^.7<;o'V?' Jw"tf (?) 

qWs.r.<a vo)*^ ^ e 5 Wt f?.C S5_^. ,j^3 t^U.t t, ....<| ^, 1,if..e 

T?S. VEU0C^Tie$ IN P^FPen^NT parts Of /\r^MS 
vev%j tie^mil^ ve.^atieti "k^lWeft^ ^V.e =^|v«08.t€.st s^.v'fa.^c v«)o«£js^i#(c vt^^JT) 

3. T^C TTf^^n y^^^^f^f - ^^^ ^€ vi^Ve&k IvaiHSvetSC Section, 
v^l, Q ^ p^ _. . _ ^ ^.(0 

tt was ^.u^d Hu.t 1k€ \cK^ 4 v^WaHon <.{ iVe ..eleofy ,1.1,,^ a^^v, ' 
^5':^lf^l£jjr— ^0^..^^. ^^«^<e d, UUw-^he soLvfotce c^t^^vd^ fe 

.ife^iww»^«*^<i a , = [0.317 d: 0. 05 f ] c? (3) 



^4-92. veuociTie^ iivj ofi^jvi CH/\WK)&>^. /77 



a^A C^^:z c^i- -^Jbv -^^O) --^»^*'VS foot AnO S&CoioP 
^^?i *v^«^Kw .veU«>. of tHe vev^K^l <u.rve. 

V9 3, <SAUCvn<; a stream or RivjBR. W\.<yc «iex- 
^•« ^=^<5,c,+ Pt^i^c^ + ^^^^^^ + jT^ ^^^ 




I 



|$^3 QAUCiN^. UNiro<^M Morto tv/. /7f 

^ ^<^^-^-^tl^^^o^ curtail ,F.^ . 6-95-, ^,J ^^/^^ ,t^, \^ 

V «^^e Hxc foY»v.M.Ue or{ ^ ^^^3 
^^^, UrJ\FOfeN\ MOTION \N A.N Op&NJ CHANiN^L, 

TW a^IKe flow '.s *T€a<ij vs;V»ev^ 1V>€ w<>.r<v <a.ssu.*v,<s ftk- 

<4 VftK*€$ <jf <M^a.v% v^^oC. l^j <%vi<S!f sectional AY <ii F,o»^^^a5S- 

^_S^^ U^il^:c?e.^4 MOriOlvJ;? ♦Meant t|iAt/t\,€ Scc'Itou af^^^^^*^- 
^e <Jrl<vii c>f rtjc u/tCtied ]><Y\w^<.)<v-. «^r< so <x<)ji«I<c( fe ca<W 

5urfa<i€.,:=r That of the. ^«^- ^^ *'*^;j ''• <iou$M<r^ for J f'wtjjlti, 
ICu^H Shdv^l ^oi^v«. ^wt \»<vchvt€cC^»»<cv^iv//f^ O/ic/tf^-ivt u^lo^iQ, 
i\.«. rt,cv« .5 h. ^cc..Uva.T<oK. Let Ro. 6'f f s'(,ow ^/r<€, *. 

^^ ^ ^*»..^ fjrcsiuvo qit 1^16 two evids \.£<U 

- ^i^r^" ' "- — ' » ' ^!L I^" *^ ^ fi<»^ce «Ck<k ott"\€V "fvovw t^€ ^dl«v^t^• 

' r i^UUotT f^ ^a"^ " " <3^vi^ Serf «^<e Ar€ Tt-ve ^v<.<'^7«^ 



%^^^ 



o^/^FOr?^A motion/. oPEnJ ckanioeu l?t 



aJd Ue /W^)^tfn V»elw*«n H,t, w.*.)iv •^v.a the 'Jo^A w^OcVv,^ M 
«aiAcs^«en -wti^s^U^ <Kj»T€>se<l «^-. ^^ % ^6^^ w^.-. 

«^uX'\^V»T^ukYy> , we t^<l.vj o^jj^Mj fe'»t fl^e'^i^^oS «s1 >>it.tia\t of «. IT^^i^i 

tVi^t Tti€ Wl^oU I^Ktl^o'*^ \t««^c^j H^ (5 tV unrfoYtvi ^moftcti ai- 
KAve 



Tey ana ^ <»ngw\))€t c^«]>tvtas not ohl*^ ok tV,€, veloctly V^tut ^1- 
SO OY^tlie sl6>e S ^6w U€ vaU« .^-f R flie tw^^v^ -X^dr^O.'c ^J^rt, 



V ft."?*. 


^ 


ji.^tr^€C. i- 


ft. (>«yS<C, J 




.0 10 97 


3.^ 


.00 1^^ 

,oofffZ 




^Oo7$<f 

,€i<i7yy 
^<yo7b'o 



§V'?^ Otv/irof^M ^ODOfv/. Kt/TT6f?'S TokMU^A . 1^0 

.ar4 for UH|>lAK«?a ifi>»lj«f ,aia A^KUv A«a breWwoVlf I 

_-.,,,, ^ ^'^" ^"^J ^^^♦^ <*^ ^^ <?^ ^^t4 s -^i <:<QtSiot,ntry 







VA^H-.;^^S^" *" secU,s 0'«-*v;H. u,n(ov«, Mor.ou) 



^ *f ^V EX/^wPL^S . JJN^f^R^AMo•rfo^f . 



18 






mc^S 



\yc I600 ,\«. sx 3^l4oo ,6V •(•. l^!€,oof^ 
Y<LsJ»ovic\'.v,<^ vol. c\«\wc\«<. |9<>-* s«<», Qa Fv~ 2 














U«V -Js. 



>N .oolS^SrX lioo ^,, M.K;.k.c.c<.t.^e.V 







wV>*,l< Joi* -_ » a 6* >^ v. '^ 20/15 / 









1 + 






o3o 









H^S\ HYiORAVJJ^tC MEAN pePTH FC?? A MIM^rAUM F«'CT(OfV' 
AU fttSISTANCE. WeViof^ '(toV/i C<^.(3) ^ ^^^ Ik^ l*f <»ih o/><n 

c*vHTv«6vi w^«\fc» vc}o<(fey V af a>l 3^dlioK5 (=: Q.-7 F)is a)so ck^fv/- 

For V to \>^ ctS SiviaK A.* ]>oss;V>^€ we r^^v^ dfis/^it The /^nr? 
of fyi^KSvei-se secr«6n ^^ ^^ ^^ vncike R a-s i<3tve,e ^5 )>o$5rWe - ^«. 
'^ «vvA.kc (He weTlici J>cv\vw creh ot iviiv»«\v»iu,s^ |ftr ««.Aiv<K F foy \h 

I^ 1t\^ ■fv*.u ]>t^e vHM.st ho^ve <:< ^oUf9©v,ci1 sKa|)e o\ H s?<J?5 lfi«vt 

iV>e >y<^?iiV l>olyi^oK o| n sides ^\M |>y<»»^,"4«. oi iw*vi«wttAm W. 








{ov a. ji*r<K F. Se< Fv^. i?^^ f«y c.n Tlx^i^. 

<^t«Ht^ <)w<Kto »«w€rs Ik w^.c.U rt,e i-K.x,v,r«v,^K<c of fKe Sft^e^ 

tftvTiovi AJ^G^'JjYoWamj -{oY Hae )6^A^^sl sto^e AS of f;ow,l<,'wy 
H«ocyt«^ SCtt»;etKM\av- wi'\t iviiue^ a ^/eloti/y of flow (s V>«Ux^ 



<}©ws od Tl7e "K'v3)'>i«^t sVfiK^e DH^ Hyc '^<tCs.so>« iaejv,^ tKiAt /N6C ,5 '»■'■'**» 
t(«» DSC . ThoTts^ F ~ vo |?v ABC = F ~ w if^v "B tC , i'.«a>^ . 

Cifli^ w«it«Y «©**▼*« ^ «*s-»^ ^dtttaU Hie rYaV)e^oi<^ jtf-r ^rcc-sJ <'.c4 WAftr- 
^d1Ue,(s<)n>m«Tiri'eAl)')S Custosv^avy Owd t^^e 'm«\ ividWsi o^ Tnt V>av,'\<^ 

CiKvUj «'vt ,lJc- VV'^ atC »\ c»vv<«vr»«A wait tKa -fcllavuvwa ]>y6%Uti; 
f^ltail^fe. S«^n*4.rh« a^V^^iSiiteS «{ 8»c B^i|»e$W<l^\ s<^.*h sf *»4 

H«»* ^i»t >*•»« <^**«. .*»^^ «.»<vr|«*w« w«*f rsAi » "K , Vf Av^ a. > ^^c^ ^«. ^<: 

«| ♦iSiiiJ^'*^- |'r*€Ti^,%'l >-^^;aSW6«r ^J^C 'Kffey^^ llit 4<?Uwii^ €faiai* | 



h'^n'tJ 



'^TRAPtT.OiD dp i^AST ReS/STA?^<^ 



lf!<f 






f»r3j}?yt»sW€.k ^rV«j J^ ><70$3 ^,v^<^ « second **i5>ri:X\?v,An©Nt.^<S^ F 






tkMji 



00 r: 



|e^ 



•i»,«. ««c Tv^wsver'sc ^t«rio\t 'HvM^iiws f tJir<dL C^'^Ck ^^*? a^ ^€) ^ 

W- f /^'^^ ^ - ^^^^**'^ ^^^^^ f>^'<w, 



jj ■ — • — ■ — .-11 ■ 






«,♦, ei^itftVion e\ Viea^S (vcaHw ov«a*c ^f 

vv* f>*<h»v» ov> tVe "Hci^ w< yvKVL*X VftWG^ 
flit Tv^e«»v«/rKlr0f,^7,ea4 i^-'^'^^O^^ c<^&. S av^ 3' ^^^^ 

wcn Won.* 2: = 2. -^>,- *^,.^ «!- a) - 1 

^ tlie section cov»sidcre(^^ whkV> tKould be Takevi siiort ^vsou^l* t^ ^ow^ 
^\AtY ^He ^^A*^^*^ MV»i<|lit UTW^^n the «v»a s«<T«V%ts <*»t^ J^c UKltir 

{\<^ r» r^e S€<tiou i^Uvtaw S«)w««H IV»« c^^4S s* VK^t l>^s>|^ (1)^+1/ ,^}j 






S ^<^tn^)e . (fyor^ ^f^^^i^acW s M^cViavilci^ TV»t Outface of ^ «»*<V 
me wetted >ttiiM€rcv i$ w^ - -jC^. + ^O - ^o •f^.^wVi'l-* F^s 'JO 

1>». s<0 ^ a x 3a. a x"5Tg ^ — — — 



•>'• 



^^96 VAy^;AB4g MoriohJ. open chamnfl 



196 



values of F, ^F^^t)^ \^^l c^.cS'3 ^*.^«s a:= 36^* <*.\>,{Y. /..sec 
Usi of H«cd due Tfe r< ^••^d ^v^av t« %Ut ^ u^ 6<? (v^ol ^^otvc^ 

w.mt axs.'e ASc f;« /;ft7 , * i •■ , . 

-£+ ^- ^'<.Jl4*« Ql) 

* 




l-.n- 






ft, Ov.^5>€<. (?^ ' 

^f f . SQvJATlOf^S FOR VARJABk^ MOTIC^M mTRoDtiCtNC; - 
TH5 DEPTHS OFWATei^. F,.,. 60^. TU iUj>* «|lhe^€cl Uc- 

S'Vj^ :::#=, K^l , 



we »vtis.v wr"il"e 

i i/>i««<w«. 4.AW f i f " .. '' ' '" 




f»^l, J 






..-..(0 



^ ^^^ir vARiABi^^Mortofv;. op^r^ qKammc^u. /g-y 




5»l« 






CHAR VL '^' '3 

4.^^. STEADY F)^c>w/ OF A <^A5 - 11^. B. Tl.e. s\U^^ni ^^.-uk/ i^o^^ 

is «^M^I|j c.i>[>l;c.^We To the ^f^«acj fb^ a-f ^ <5^Se^c.5 flu^c^^ 
Wt wirti^th.s aCffev-R^ce m s^ts^^c^e^t work Hxcct tt^e ?l€ai/5n«$S, 
k C§7) H'^^ 'J'*-^ >cL$^i--3 '^^ff^^^*^'^ s€<.lR6*v^ of the ^«>e ov ^B^ain 
(me h ov »v.^^ ^^ al(fev^«t riKou^k cavu^.js )Ke sc<v..<e ^ ^.^^v^ 
^w ]>oivtt ov 5ec)rov,.,v>ce Ttie fJow'is ^eo/iv) For Hie.'^T'^sevit w< 



^ ^^1 ^T^APY f'kQW OF GASeS 



IS% 



I.e. rt,c wei^ 4 (^a.^ \,c^ssi^^ c^Kj iccnoK^o-f Area, f^ /,<.v u.nt(i <?/ 
"t'^^eji's die ^^^'-'t as for A^y anicv sedt^n or Fi;|. - cowst^nt 
j-bem^ the Heav'W'isS ot H^e"^ Sectiitt,avud v H,t vt)oo^y . ^ 

d'OO, Fi.OlA/TH|R0U<;H AN ORlFiCH, RFT^t ARKS, I h Frrl 
G06- wehAve OL larj^ertgicOecelvC). conta/^t^Vi^ (jctS at So,v^ I 



70 V\ 






stvU 




■^>ft 






c, $fak IZ , Tlie wy^X orifK€ 



Hie -J-lovu \?«co 






ovuiK< 



^et ntn ireji^^sent cv,^ %Xy^a.^Ax;,e (I ^&*^3 of The flow 

,'r."5 ea A j.r o,^^ one IWme., eack K..,..^ cJ Ike l^.c 
^n^ e/.W C^.^ .; ;. We.^), c,. Tk^tyront one kM <.t le 

iV \\x^ throat "of "iKe jet,^\>e veWiC^ W l<c6wx« i; n.^ 1, .c^ 

OH the le>^j>era.lu.re of ti\t oufiide oi'ir at-fd ^^ u>hi'eh tff)uj( 
lakes ;.We,ni<.i<,U^«f cau.>se,a{l<> rhe effUent ^«5 I's OKt< /m« 



^600 Br^NOUlU'S THEOREM rOT? OAS^S l^'i 



<x\»lw On oxcownt of \\-\t tx'jjakyK^io\i a\ U\e e[{lu.enl acn$ 'bcvov^ tV,c |Wmi( 

;:.\,a . at a. J of -jrie, jct (^ e-^^^^'i to tUctt <r( rtxc ouXsi'ae 

,'^^'' »nccl\u.iv».. the r^HStoii ctC ?n is ct\caXkr W<a.uj^ 

V^^^-^— ' ^^^ ^3 ^'^ cuyo^ "(liavvtftHrs "V^rvwecK ^^Kv^bTll, 

^ 40|.FlowTHRoOGHAivroi^iFKeiHtAVi- 

FORMUi.A.1^ >Kt !.^KeY i£K*<in J.^ ex<e<dis IV>e ouJViy i .Wet 
i<Ky^*. WvmeiS <iu.r;>.5 i^"*' " TUk, jot the ii,««lUv,«<,^i aAv«^ 

?.T.r~-^ vtP^"-F- r^ =0 t-B) 

^OR ORlFlC^Sj) J «^^ J^ ^^ ^ V. ^ 

W ^^X K= «rW d.,r,KC. iv,^ ^ r, ^^^^ ^^^ 




in »» r** 



*^^^* ^ *^ ^* 4«<tV»o^«ja «.r<a.tf{ rVie jet ftt m. T|tl%enwX 



^601 " WATER F0R|vh)i.a" f^b SASES 



?0OI WATER F0R1VH)1.A FOR gASES / <fO 

■\t<Cot :,r--\:c£ 1,as well yaund^ .hI^.,,^ ea-^j ;k ^^^k- , ^ ' 



•Htm biS VuTTJ 7« cf" -"'T ?' ' f-"^'^ ■'''" ^^ "''f''* 

weWvt F^c CF =o.6oF ., (^^ O.60 F v^. .. ... .(5,) 

n _ r^ r- ^ 

^ F V ^- c^) 



■-i-<?^r- = f:,.^^„ -^.^.n 



^Xampie.. in r„e resT.«j ef « b)o«,.W ««^me it ,4 found t^aU<o/ 

I '= " ^.;~*« .^ i;. ',V : ■:: :!■ •: ^- v'": At- '-*■ 

c-. . rt , ^ ^■- v5e |t. )V>. Sec. 

I ?7% <n rt,.s wotja ii,,^.^, ^„^^j. .„ ^„^^t «f f»,;ir.;,T 
S03. Flew rH,?<,o<;H AVoR^^rcVoJrts'ts""^ ^"^ ^ *^^ 

u„.w.,Ji;:;;;;^ue flow C^^ ' "">«^'^'^ >*-«^ 

' _j 



§60a FivOW ACC. TO MARIOTTB-S UAvV | ?/ 



CO. 3^ Wut Take, cot^e to note rhat^-noNA/^ Jr is vol^\o^\c (,.',«.. ci;f|cy<,^ 
fff 6^ e^.B bec<jtv.<s 2^ \ ^ - h^ Joe. ^ /(\ 

As Wjov< t^^-^^f ^3<..d flow oi vo)u,.. Kt:'t^ Q^F ^ -^(3) 

WCiGj-^T OFTH^ Fi^OVJ PER TjME-OjJrT%. C s F V jk //.<! 



A _ 

n' )?3 h i„ I" s |^^^^J^^5^HIi^X«oas^/«, (ill 

N= .O'-.r lb5. p.v ..V, ioot, ,, y^, ^, -^Kt >" ,^ '*• X^, 4;«W,e 
>«r C<«t. less ^UM. rt>»t ^!»<» V),, !»>«." w<xr«» ■{9>Mu,la.".' l-j Hie dvUtr- 

403. ADIAPATIC EFFXUX FRe^A AN 0«?!F|CE. It .%.^o»Mm. 
icai IS a.MUme 1kal ttie tK^ansiow »| Hie <^<^^ ^K»fo<wA!iw<j Hit a^;. 

'b\c:).t is more ,a/;c«.Y«.re To i. <^j v«.,u,w« e^.t. VoisSOMS Lawi/ 



^ 603 AD/A6ATIC FLow THRo'A M ORVFICE l9X 



ExatnPe /. Let rt»e mteyid*^ c&n^'jDous Tm. IKe ^^y^^ t«sc>vo4v 
o|Fi^.4ei* 9ea$^«Uovv5 ^s/2>/^ ^?): jb^^ 0,%'/^^ )\,s.^my^A^^ 
Ok3 T^ :z a^^*' AU CckX, 0^' ^'^^ Cc».t,) 5 '-UiJt ej^l^rnal- 
^>j rKe rik^Sioi^ «S )^ y^^' ^t>f s<|. in«:K vwUick vv^Ai ^< Ia,k<K. ^S 
-/'ii-, ^ ^sk^iVh «*t ?7i the, thi-ocit of jet , Th< o|j«»^t»»^ is «i CiV«/v- 

ot^ \\^\. .f T^= 2?¥^r = ai-7' aW,. CiKt . ^ ~IC C^lt' 
Au^ o{ A. lieaviiiess /• - O.llQ^jJ f3u\'^ - (;.D8r6 lU. |>cr cut. f^ 

^ l^ttie two ^r^Cfidivi^ c^J>^YOX. \>v4rUodsC^^ ^^^ ^'^ 6<3i?) 



I 



in % 6*0 1 . v'- -^re^ et^ H) ^ ^ ft 

^— I u -— 



'J 



O^f 



['-^-"'■^^"•- 



a^<i iiv*<t ofc in "it 'lb oi << li2XtvV.tcsS K ~ ,08"^ JC~")^ -,0*7%-^ I 

WSICMT «F FLOW Pt-^SIJ-C,^ a=Q».,K= ^.^ O^X-O?^? ^^^"/S^ ^ 

B*, tSaft'i^dJcj'/'orrp.u.^a." Q=: 0,^2. its. >ey sec. 

v>'OV. PRAG7ICAX, NOTES- THEOReTiCAX. MAX.FtOVJ OP v^;t=iOi^T, 

weiCKT OP F*-OVU ).^r^C) , -F L s T. "4 V V, 

PER U^flT 0Fri^Er^^^«l---U^3>orn[»->^ J>^'-^^^ 

^^ ^-1>».'^k;^( J.) ^ '^'^ (^i 

R3.6o:>)U tnaa^ t^ <xssaii,c Uvu^v c^vujl louiev v«.Ws C'^hc'- 
"K«vs^<. Xr >v>^ -^ j>». To cUiMm.sK 'jvt tV^e Sccme votn'o rt\e '>v^c^afivviKn^ 
f\o*v of w«^>,t >ev u.viVt ©I ti^vie w\u etcu.^ VA3V»<w 1> =: S'/O > 
c.^;>fk »v,ore TVx.. hc^^ the m^i^i^ fusion . (w;-.-!, tKe ^o^ acru.C;;, 



\ h^ 



Koit cUyeai^ '^«^*^«ir«ct ^c»t it tou.U not AcruailY occur, ttx \%64 



K 






t Ke eryi-'-iHfiftiou lies ih "Hig ^oct tViat ^€ j^reSiure iVu n>e Ccn 
Tre <>f iKc Cci-xl^clicL jet IS not n,esar»a< CcS XWU o\ \Uz %u,r- 

svo^id^j^ ^^cK^s.av^a H,e cUv^^e of airccliou <*{ Ue {)uaM'"^ 

cUs gc.es V,.. to cev,l.Y.^., force. ^ wV.ck ..ks< fKc ^^.s. ^ 

U.. V7.<.. , ,-,7^,, He .J.. S.JS - Co.r...i;j, .^ f.cEoC 
»nM.a ^^ allowed fov 4 (he u3e of c. <:a.eff,c,ea o^ cJ/s^Ur^e 

r^.^^^. 1?«.V.„e ^,.^^. r.. 4 ,K.t';e tCte j^e 
or.^cc v.«» used m cc^f,uT*r,o„ mdi««i of t(,e ccHTx^efJ »«. 

FOR ORiFJCeS A^JD SrtORT Pipes. SMAkLOiFFEReXiCb 
OF TBiNiSioNS. Since Ihe ^vscl-.c^i^e tWro' ^wi ovifii^ ©^ short 
>\i>e ivotvn ^ reser^/oW 1$ ctffecP^a uot ftnl*j U^ C6l^W<aa't^n l^^X 

. % ^ V : resuits for the v<.Uv..e cc.^ .^e.^^t of fU^ >,^. ^ 



^606' COgPFlC^E^JTS POR ORlFlCgS^eXc. I^S' 



CL Coe.'('itt\'««-»t 0"{ velocity p o^nd one -(or c<j*,^Yacl<on CJ . c»> ih 
tVc c«L$e o-f waTcv« ,\e.\»»j a. Coefficient of eff^ujc UL ^ 6 C , 
CC^ course, \/^Viev^ ^ere »S n«» <onT>a.cVou^d ^ ],o-o «i,*5 tUcH M = </ 

Hevict -for ^racVco.! ireitOU jwM^, ori'(i<cs «vvi4 %V^oyt )»a^«^ wc 

1. ^or «n 0rift'c€ if% » thtti ^ia.% , ...jut x:l 0»S6 

«/ /*>r« Cff *?/««/ Tuyeres ^ o, Wo^fh^' y^Achm^ h F^ 3 ^f, if^^hes ^ ik\ 




ag&- 30 ■•--■>• ~- -.-^.«. lot (.«..' -..v/^ if. 



7U-^er*7./Z-5 n^ .?2i.3iy,,.., ,_ 



w/:<)e r= ^3^,, ,. _^^^ *^^(:^ic«; M= -.*?:? 



'/3 



% 6'Oy eXAMRtf. C0'6F.S OF 6FF1.0X . or\f{ /96 



itc 



r.e. Qzi .6076 Us. >«r second j wU.di. w;u J<:cuy>^ a vol- 

506. CO-eFS.Or FFFVOX For ORinceS AMt) SHOftT plV>/rS 
F<5R U^aCH DJFF)?F^E^/C£ 6f TeNSiON, Foy voices > ^ 









4= .VjM~ -^^' •^5' 


.^? 


7a .7^ .7^ 


♦^ .S; ^^ .i'6 ,^7 


.$¥ 


.6^ .7r^ 



K '* !?•,% jf'iv'di decreases $\i.i^VlW fov mcv-<o:,s,Uo Sfxe erf oW'f.'<€. 
^///^ short cy^,vt<3fVfca/^/^€5, /V?/ey>,ct/ ^^€s n^t rcuyided 




^ v^<>^s -jou^a :s 0*^3 ; wKiU c». well Vouvuiftd moaIii-j»/ec€ 
to ,96i J fAY ^^ rj>^ vawginq fvom I.HS' u ft-OO . 

507. TO FlMiO THF DiSCHARGF VvHtM THl? llsJTfc^RlJ- 
Oft PlPS jNQT MVJCK kA<^C&f^ THAN THg QRjFf Cg ,K^.^o? 



^SOl 



veJLOC.-aFAf'Rt^OACH 



197 







Fxa. 607 






hi ■- 



Twetw 11 a«d in-ij cv«i iW*^ vftiiCi^ ^ i.j t si^o^^i Kfl»o< Joy QuJLaSid ^ht 






A. Move ^i^s7 , V _€f^' i 



1 .V % fV.' ! 



Aye^i 



'He 



4i b«"JotC 

1. = !•« T 

^ live c<.„rv»cr.i -»«;.', c<«a - cf , •" ' »«a«>.«.) ».«. 
£x<xm^)s. If m* <!.„„. of Ae,F- 6^-, •, :.,, '. L*^ V; 

;; ai ^^' ^ ' Tin. ^^^^ ^^^' ^" --"'',-w, !u 



rt — 

j§5 07 VgkOC> op APPROACH. (qas) LoajC fitpgs. 




i'OS' TRAN/SMlS&lOW or COMpRfSSBO AlR 
TH«0' ^SRY kOK<^ kEvEk PIPS^S. Sxe-ADY FLoW. 

"..AJI"™, ^:i£<7Xn\ *l^-c*sTt.5 

[.y-^ -^^ — -i ;> : . T'- sin*>)ev 1; <>k- 

Puttn^o (cLi aU«« n>«nrion<cl3 'C "" \ = 0^ vMt V«.oe *vxoye SimMv 

Vif2i ^ ^ii.i: . _/5i 

50f, TaA.K4SM{S5!OM op '*:' ."'SSS^OAl^. ^Xpif RiM^AJTS 
IN TH& ST. GOTHAR^ TUMf^^L^ l%7^. [Seg J».9g of Vol. t^V^ 
{^FcW *§l)j^av» iNToslraH^^ 6'.^^%t4*?ri«^ Mag|C<x.jU€^ In l1i«S€ C^^<t- 

^^elwercd Wit co^\)v«ssc4 <mV to itie bortv,Q.*v*-^«i„^eS' %*.«€ 

^ --^ :- — : -— . .. .. ^ ' ^> --^ 



% 6'09 Tl^Af\)Sy\>SSIOM OF corv\ PR . J\y^ 



199 




«*«-« 









F W>*^ Tt^<l Se.-f.rcG.^^j area, at VW^tr [jo^nf . K^KC^ 11^4 TvreiS^H a/«/oc« 



*r 



rtis >'H v«ko:j< c^i«?5>^. =: i3 ft^^ l^KA^k = I . 3rx ^ITe <U4«;>-I^*r.ts <\)l^ 



/6095 i % 






.376^' 6\^^ 
.3oo<? 4.13 



3.S3 76-3o 5j" 
3. S^ 37. /3 X6,S" 



3.66' 
3.S¥ 

In "^ 

Itr.tti SK^^n C...WC5 c^ ,V<:U or less i-4<U^cJ^^ \?U'e.*Ucl, 
for stiU Ht^k^v v^L^ec.fi^s 'f w*^i swv^*v\\ev^ *Hi>^*s»*H^7«L^ 



.e<o3^' 
^00 iff 



iC wr.rey cowWl's >>u>*%«lf H/\n> »V»«NA»ing '^aI . "We^'iU^ij^l/ 5 va.iu€i 



i ^ m€uiyid^»uc wilk ilae rei&Tto^ ^- .06"^!? — (l/ rvi/t« j» sec 

: «.» *r^.s.,Wc >v.^« te^^, r*-rt,e j>-.|,e fce.V.. 50° FocKv. 
f ;. Lft. sec. 5 *»c i^.*,^ v«S^«« J«^5^ j=,, iec.iU ft« 

|*^« ^ir^ A...-";|--^ - ir -■ v^-, ----- .4.9) 



{%k^%'i\ l*V- •*■•?>. Sf: 7 213. V ^i. - „ i*'^«- 



^/0,(Ci4eir ^/^i J'^/j.^^wcJT, COMS4/>6ftAB).6 OIF 
FCRBKCe op PRSssu^lf AT eXTReWTli^S OFTHf pjpif 

— — _ . — Z — J 



-- — ■ "Z : I I *. \ - • = 7L - r . 










<=*>_ ■Mf G"*^' 



I e 



-/"^^ 



_ '^iQ* 



aoFV 



<2s <2) 



Si9fi hei'H.f j^ fT«^ ^^t ^<!J^« *<^ V« itc h€<!ft ^e«<?A/i^ 4<f /?»« ^nc - 
t eliUWY^t, ^'/?c &>^ >»^5^*' ^<JK<-< iv& nnCLy Trcut the, -flouj^^ i^ctHB^M 



^Jw 



C<yV 






-H 



is ■ ~\p<>l>~ 



■^K/A.^ 



as .-^3) 






ISOTHSPMAi- 



k _— — 



§ 610 AlR W long PfPCS ■ LAKce FAU OF TfwS.oA/. ■?<?a 



2r «»'<»/»>'«. i4 */«» or »««,.»*.V J^jl/,«i ncturctl qui ^ A.l^f 
^.>*:^. ^ h, tn^hyi4,^,.J the ltU„ok ,k tte >«««»»y r««<.«V 

,««/ s, ^«' >fe>.^ 5; ,4 r^(„a ^^^^ ,^^j^^ ^ ^^,^^^ ,^1-^^ 



•»^ i^ .006*, 






OS 6*0 



^73 






Qs: O. i%'70 lts.|>ey iccoHct C^o*" <'o«*-f)>«ss«c( a/l^os. ^^nV^MH- 



%Sll 



'■RfACTIOM" OF A itr 



2o3 



CHAP."vn:. 

Imbulse and '^esis\anfC <^ Fliuis . 

6//, THf 50 CAU.&D •REACTlCrJ*' OF A 4^T OF W/^TER FU^ 
ING FROM A VHSSFL , \n f^'^- ^'^^^i a. ^r^<Vion\e?>s V>«*t waW- 



ft 



V---^: 



Jii^i) 




aY<a.<4 »>^f»^) wWck Jv 1\,ft <««ii of ft»€ 
, noYixoni^l H^dYOsiA^Uc W<s.su.v<i r«w«^>0C 






-p' =:^ FHjr 0) 

°Hxe vtsstl WDuia. \>^.fij^V c^ **n'*.joYmU ^.^i^Uy^iii ^c^q%x %wi>^'r<k Vnfn^t^ 

M i4 Uto* tVi« orifice ,v,ot oYd^ \s f^ie ])Ttswte FKj- WV^^j eJtVte 
H-Jt,oH.tti:<6unt ^ rtie oritur J \>ut tV^e turn fei Ht4 >l»rV.;^*hhfcl om-kIdoh.- 

vessel wan a.Yoa*^oL \he oYif'ce K Uss tV«.vt. Ms voa«Afi \»ef«Y< mcfU^ 

W^O Csct n^xt §). i4twc< a^^Y^v^ effi'^v^.nie 'resu^ro^Ht Wtp^t- 

TWE RgACTiON 




Fi>^ ....a) 



OF THE J5T J 
§.6j5/Ri?ACTlON ' OF A ki^uii^ 4ET CK£ THl: 



^SlX MAkOS oPTHt^RcACTtOiv/ OF A- JET. 2oV 



jUst U tk6^o,l\U€ R,. 611 «^ feen -u. ^-K. Also let AM 

W 4t Ka. W .k reW. cW^e4 f.on, z.,.c Q.,l .W,d, |tee 

fiVu^^ ]RaA<tWr p-^ 2rh^ - - O) 

•^ >te.ce CS J radices to.... - • "? ' - P'^^^'* 

(sec§^V) r*~ a^VA^ -(59 

BxanjJ^, lATeoU^V ^v^ev^tlov^s rl^e e,f^<y;w,€v,ls ^^ Mr. ?€liv 

wJlV a w€iUroou«^€d on{ue ^i i^c R^. 6li . He also *" r 

V**^**^ 4^ ^ .*1f*^ -for the s^n^e OT.{Ue ^%o rvi^t c^.CV) 

W;tkcu, oy.^,i£ r^-n,.^>pUre. Mr, Ewayt ^,«^^ -p,, ^, 

Hue co«Jv«lea s«.r..;. .6V F ^4 Vi-4t^ l . \' \ *'** "^ 

8<A -vesuJls a^r« well w-,tl, e)r|>«T,Uent . 
613. IMPULSE OFA JEr OF w/ATER OK/aPixEO 
CURVED VAME C^'fH BORDERS^. The jcL t>aMeit«««h- 
Itiolly u(.o« me vane. iS^. 6tV. A is Ihe trartohav^ »o;^^)t 



UM - . ■ ^- ^ ^rc_^ ^^^ 

-«--. -"—Xr*^^ ****•*!( ^»r««>oHi^Th« veU«iU. o| 

>ctwfluvii =: c fat cOA )>oml's eOonq 
iVie cu-roe. Coviceloe U»6 Cu.t«e eVoiacd. i>,fe a,<jv«At r>ujvilitY^ of 
^»«00^ Itv^lVtS 4iack =r a&yvi^ ^u\,r^vi6mQ Some ^KCik ^ c?d (^o^ 

Cai^jcy«v»t jor aiff event ^Ss's) ^V»eU wic^^es iotve oiwt^le ^M wMi 
time n.cY€ is ciK arc cf ^^o^Tay^i^ Covtrcet VMUi^ the v«ne,ex€v"t- 
aijcuv^sl n>e s.v.Ail mass ^ vuoJcy f ^s^ ^ j ^.K^,.,^ ^,,. ,,^j~^ 

aPs [FdYfgJc -fr CO 0*«>7O 

fe>4 av,<f U The ii7,>*J5e or ^r<is^r* ^ ^u .^^i ,^^^ \. 

v«)a« 6-^ dX, we oVU,;. "m^ s^,. oj 1\,e IT cow.).ene«ts ^ 

1..J tkt <*r< of vvoTev rWtv. it c»Y,Tact wUh it. I,t-,no't«^» tt.«t cH^v<i| 

'^e X-IMPuXS€ 1 c %^ 1 a ^-r -\ 
Aqr- F,xex> v^NiS = ^^|- IJ- ''^'^] - ^D- '^^^•{l <0 

ivw wlitA © 5= Fc is 'Uel. of water wli^eW )><:fc>$e5 *tW fti^ i-^ox- 



^ Sli IWPVJvSf OF JCr ohf VAhi£ 



!106 



a\ iAiVeclu^ii BA 4 ^^ j^ ; '•^' «<•= ^^^/ ^^^^ lyf e^iflk- 
flon Simtlayl^j 1Kc %KJt^ of ^e. X c^a^ow^v^U dfll^e 

c\P^5 o{ FIj. 6l^ t>^a.>j W sKo»vK to \>e 



\^P '-^''« if ''^ <*»°,F-5. fel6,>«cWo«.t•=o; 



'1 



^^'■- <%| 



4e€a»i 



61^. lMPUk1>£ OF A ^61 OM 

Tiorvl wHD^e AXiS iS PARAkkEk To . e i . 
I^ Hie cuYued Vtfivt e ^ With, ^©vcIcva, *( ttie p 

w'vtt, its axii iw ime »f H^t jet , the v^sv^^Fc^t f^--^^-' 
>Tessi*YC oi «,e Jci i^oH it w-\l{ s'l^j,^ i,^ die """"^^"^ 

>r«j»u.irts ona)» e)e*vu<yils of Hie 5i4>f<^.ce at i^^i^/cn. 'in$r«iu( 

'"''■x-E"= QrvC'-*'*") OS) 

VvhiU Hte Coi-w|>otienU n T* Xj alX rofliiaUi.j ^yo\>, tilt. c<x\s of 

Fij^-^lfe-, dt rt'i^Vt ci^t^lei r^ tiic jet vue Koa^c t^ .:f> . 

(5 n ; 1 




'Tn-<^ 






r~^~yu+ iMPUk^E or JBTS ^ •i^o? 

' (^te closely. E^X^) 'S Q."b^)ic<xWlc '^ fhc. tV-.eory of PUoVs Tw^V>e 



I (set § '-^^O^Fv^. €.^% i ^e «o 







i^ eit Test <a^^;' ifs secHon ^*t* m 'iv\tf<y 
j Ce?viMg r>ot OV^lu !ti6 )^^5<iTOsWi6 }>r*sS • 






.r 



F>^-H^V « F^^-t-Fky it. c.i^ C7) 

«k^ iii^ jft )i6^^ ft ^i;«ime(liy «f I u.1.1, >c ^^**cdl u;^ *v^y,:r. * ' 
HAVING UKTfRAl^ BoRDfKS anj:) Movih/G. iisjTKe iMRBcrtoM .v. 







{Jo UvoixL ^J±^iitM dtuiatioii^ the «i5d?cj6 T/Jt)<-,^ (S y3 )ot lit 

c«X A ;? ^ C-i^jlU^i -reWT.'tfs velociCY r<*voC\^s %s ^i^s o.- 
^CH/j fli«> luMte. j |oir -|rtcl/«t» i4 ^i.%Yt^a.yded ci*^ the aJL^*!- ue^o**. 
o{ tact\>a^t o{ thz -v^Ktf Is of ^eke S^i»t^ «K^<jc«Hr a*^dl*r<«/r«i 
ai erf aKj o^'^icr I^Ar.8. l| H^ft >wdTIo»i ^ tKe voi«< «4/cre >D?^ry 

<XHet\v4;i or( M'^ '^ ^f>}»VcaUc Keve ^{.caliv^j C<^V for l^e. c 

coMpoMfeA/r OP jNiPukse 7 c- >.V i 

oh^ t^ iTie 1i€Auin<s$ (S?) «f f>»e )i^<<.c<!(. The Y <o*Mbon<.tC 
Tov *? ^ e{ Hie 'vcSulllxnt ivn^ViUe )s CouwUycic^ccI tw t)»C J^^^Jrort 

tanked <^'»^ * ^iucKv VftWd^ z: V^ iRe vo<.C^l»t <3 tn^st be hr.a3e 

]3v-cS€yc^ cc )jTAcrica.)W 7ior«7.o»-ilal «^ir€4Uo»T jfrTr ciw ^Hcl<{imtc d(sT««Ke 

%C i«t J 1; w^)^ V>< he^<^iue Kt. «^. (OjVkJ^ik^ J^, (and »\ ^) 

As to TVi^ ^^^^ <»/ ci/orU \h% 1*^^ ^^c.Toy cifcVioivt^c o| 
^vtervgij ^ iacnA/€et-v4lTe Two \>«<iie5 jet ^l*'^ i;Avne , dccvma fit m.w* 

....-_: _— T_ 1.^: — 



% 616 Work OF JET ON VAWc ^C? : 

:^ r— V — ,- — ; — z r : : : : ^ — . ' — r 



uWtt of tui^« ^j T ^ i\e.fftA/>^^cr ( ^ ^^oS tx^rf*^ V Tj^. 

Sou^c MeAoc\ru ViH^evc the HT:*;. of jet mTerc^W ^^^^^^^ 
Two ^anes ^S at ViWevf^ To {imsi, \|-s wo»U or. TKc f>o«t v«ii€^^J« 
aWiiJ.i^al worh W bW^^ aohd OHlV.€ V^^dey ot^e j U Tkc •^•Ar 

F(C-ll)^tVi€ vol, •^ "flow - » oo<LY H»C* uane^t^ <<^^C^) , 

wVie^iefe, POvueR tXeRT-l T^_ O'' ^ n^ ^ x, > 

£D Of/ semss OF VAwes ^ "^ zI[i-CDSDcyc't)> - —CV) 
•II .3 

wff**^ IV\a1 ivY vr ^c l,'' n^e ><HAi€v '»s ck mccyuixo.«^ . I 
/\ssuiv\ina dtWevcMt Ma\a«S -fo'T fit^ we -jivtd H\at ^ov c«.-SoO^ 
ut-Vj^lh^ ust o|a. se*wccircu.W vane , or o^ ot ?)ei>K'sjl»h<v»<«f 

^ . Itt wKuV M* <*cKc/r€i rhe mass «f the ^i«w 

^j //' Ftj.G^^ ■\u.rn^*sVedl \>tY unit of We k^ tlifi jct ;Uev^<« 

(;j T1\6 ^woW ttf Fl^ . Q,%X (jcnei erf /• |»s^ Vt^-^ ct l^sat^Ko} I 





w%U not o< aTUm<dl^ ' 

516. THE CAklFORNUA^HURDY-GORoYr^iR ?^lr^ON 
VvmtHL. TKt efficiency ^ urxdlf U Ihfi sevlw o| ^i^^ p^^ 
n,ev,tiori^l U \. WcW Ve4acJ To g-O ^ ^^- ,k. cell 

o( waTo. Tke Pc)Kh. wheel ^ *X — 0. 

lvieehcm(Ca\ ))riHCi|»)€ just j^r^* 

tK^t M/'iOi [ht y^Htctf veloctty F.as6a3 

-t w -v^wfe r^n,. -r^:., of n,e wwi(n%cL, 

•««1V S*.^ »)»«•>. «f TroUU; ^.t. -r^och.^*^ »„\t «f U««J, 
£Xam/i)e. Tf n,e jet .h F;,. 623 \^ ^ vJoe'.lO C= 60 




%SI6 



<LAMF01?N)A " HOROY GOROY" 



211 



1 



tc 



8i 



r^ ' . .t«-T o«.~ir^l*0 fort, tLtp-«e1o«'.t«* 

ftn^ular ve^ot.tj of ^e wK«tl w\n We -w = D-rr=3.o 
radians (jf"^ -^M^Wn uc ex..V 5t <*/0- ,.>- ^,,j. vcK, ^HOJ, 

wKtek neavln = '«r,'^^» iw.l.l>jmj "«.vlyU. K<i4. >-ce.).^«r^e<. 
3n OSUQOe IMPACT OFAier on a CAOVif^G PU/\T»r 
HAVING WO BORoeR.. c;^ -■.-^^-■•" . "i"^;^ W-^*,*^*^ •*^'': 

jet ...7,* >^ ....^-%<^ ^ ^xaivdtUiu U tojel.wV.s*. 



<^ v,c\..f 



vetoc'ity U ::s c , At O iKe 

^tWe "^UTe T^>^u ]>arU'c3«S are aVL 

\'i\;///y^ t\ the V^Te sut-fc^te , WT n^^ 

Vc^jxtcWe abs5)i>tr€ \;e^6<iT*€S <>{ tlie^c yoirtieUs d€bt>«<i o»^ rHe 
-\V\e velotil^ 'V of Hie. y\o^<L , ^^y e^c^wt^ le at B itie o^scW^ i^e^l^ 

IS the ^a\v\< awd - 'U Slnc< . TW ^kirt-^nc/iAM *?{ tlic '\i- 



%fi? oBJLiaof jer awd ptATt' S/z 



«nl itj a.v,ou».t ^ "P, IS ».«it >eadijy found as -foncws ; 

T)«»uJ fcj AM «t,e n,*is ,fUe ll^uCi )>o$j^ »««>. (!;« 
>lai« -iH. c short t,me At, ^^„)oe H,fc .».„Uft „;j,«.|.« of 
«1 lil< K^uU ^«»r.e),s ^\,*fo»t a^ of,,, J,„Jar.o.,^r>,5 c^inikoft- 

y>Ao<i^ ;* ft,e dfr*<f.^, of T of c^ = C s;^ o< J o».l«»«- 

H «•« H-^^ * "«!• - -"V-f Y ^ U s.\ ^ ; fl... »^ 

'\ ].jl <H„ «^^u^t of T ««lo<. - (c-i))5.wo< mt,«e At; 
J^.IWy U-e S.<tY«v.<i ^-.„er.ye r^lavdj:.; (oy n«* «- 

^ - t"-»'.o, II «i Y 3 - At r»t^,,^ .\, ,(..- 

J Unit of tttrte fndttJiwt iw<«H« (voim ttoziIe'S 

^ wUjtk F * S«<r<6««l «><* erf j*t k«fftr< n<««Tiw^ ^Ictfe . 

\jt.B. Smw «<|.(0 can alio U w/.lt^K ?= M <».«« -Mvj...< 
W Mesivtrf Yvx*j te coud Ac y-Mei*,tp,n»m Ufoti «»*- . 

•i U jowelimes soli r* \,« ^(MMditi. o.,n,e | »'iHc.l. le of h,.- 






%sn 



mpui.5e OF JET ON oauaoE platc 



-2/3 



to ^C dxrecuon o\ tvotion (v ovi«l c'), oim^ Ute oHitV^ P"^~l 1^ iKt 
Pc HsuvoC^ oi C<^-^)iMxc< .C?) 

3 
foYCt P** decs no v.fiTV ^wV^ilc t^e -jonwer ? , <^c^ an sJi.r*»o**w.t of 

(out PJ.AT€ J g 

U msTo^ ft{ fitsmqlc ]?UTe , a series o/^/aT«i^ Jotiv%\h<j a. xjuu 

PowiEA exeftT£o »^v Jer^^^'^^j.^^^^-)^^;^^^ Ci) 

0K» se«*r5 OF PkAxes j f^ ^ , /, 



2. 



<_ V4.0 



cL ^T^'^ 



'"W<lK 



3 i- X a 



•c^) 




POkSe AlsiO ftesiSTANCE. l\ ct TUt;,, \\ct ric^id |>]ftjfe. Vioueo. 



tvOrA iotct wot ^\iaw»n \w -fcaut-c tB |>Wt 
5cru« ttie unljor*vt mottdu^ considmj 
erf o*. n&r\Y\«.l cow^otTent Ki "1 fe|>I^ 

Wlicvx ftie yiale <xw4 {WuL art at v-e^t Uae preSSutes 



§6'l«r taovinC plate im fiuio- ^^^ 



3 



<^l»«Ilt Sfdc5 a?e iT»ri^«i-^ A^d W«i«<< c^xcW c&O' ^<m j <>rcliii« ^ 
ike normfld ^es5»urc$ «*« %^ fr«ttt sa.rfar^ Arc te<r<AJeil \t^ 

%a^ Surface^ 33 ^ tWe \\*jUA, dots not cVo^e m f«K$t eno«AAK fo Jw- 
dUtfC ^ )>rcssc4re fi-fuxj Tc fnol {^t^ «f rest. J^ i^^^ \^ fj^ r 

a woroam may Ic f^a^Ih^ed hehnui the jMe^;^ ^\CJk is^e 
Ikcrc b evui^nl^ no -fen^^r^ Pressure, frm^ hfkind. 
JY)?al£ucv pressure <xxJL^ o^^ iVc WcV «^^4 <«5»*-^«^> ^ dimtn»4i 

Wrt^ FviMvt 1K€ accomWi»t*»e*dt df Hiesc e^cS^ Hie XifJawcc 
tit ft%»S <^5C (ei IftiSt tHc ^mJsoHCwtt N -Hortwkl l« )»^<*^) »* 

r^CV€ 1^ |c%n*«i, i\t.^i{ the fl***<i «octl<i close 1^ l^K^ «»c 
SiMooQt C44)roe<i sTreoEm- lines SMt*»*«4irvcfitl *i^A. fc«»€ m fto«tC. 

Au€d. m the ^rlUt of^ {liuacfccrexi o^^ V^ the -A^U fncTw osrn^ 

I^ 1^ |l«*iii IS Seg^ wafer C^e VtSuJili «^ Col. B €«fi€^^ S 
TAg resistance ^er ZQuAte foot of^yeoL^ ^uitkti^€d i^ ^ 

i^n S^-^uVey uj^ik. ccveloaly of vz iO fi.[,ey iecoiJ is 1^2,1^5, 
Kealso ^^serS ^ha.t for o^ey velociFieS hie Ttsn)ai^cc vart'es 
CiS the S Qccgyc of the 'veloaty- TWa Uilev ja^ct y^c^ou.U l^^ Iccl 



§0^18 PLATES r/ioviNC IN FLUioS 



Q16 



^eVs • olva \^ \ i'H C^^t ccj^. 63. AUo fhut ou-^**-^ ti^e ^Ute -^r^oo- 

^^^ __I g- s Hie a«<.e^€v«Tiou cr| ^?autty (r 31.2 jer Htc fdoC 




.^ 




^, ^^d ifco-rtD 3 ^ ^.^! for tKe met^e <Arui see© 



TO MOVING PLATe J ' 1c4 fo -^ 

fixed h')cLfe(^ li MeSoQ. oj sVy«oikvJ),v ^«m<j H-ie ueloMU, of !V»t curicv^t; 

JMPOVSE OF FkOiO 
UPON FlXtO PKAT^ 






i 



oljo C^^jrou.v,4 ^c^^coT^y l^j>ovUnce) Sv^vcc Vhe co-if^<cv<v4'^ <x*ca 
"^ toVxVcV de\D«i^ OK ex^eviment Ave CviUevitli^ cclazjyad Ticei-^keys 

UJcJky[li. 7^, sac.] yjTiU^j R^ naUs.^F^ \ ^?-f^- ur6^ 
iW'.'^cv cuL>-ft ^ avt^ >J= iO ^t^^ZY Second J ^ 

/< aXSa.^Xnl _ . o f McviCe in ^<^.0J for Sto^^A.rJ'eir **.cl 

Cv^Iev o^- a./V , '^ _ /.26* -for 6(j\ ^n;,\ vw'K\cIt 



%^i6 PUAT£5 r^ fko\OS :^/6 

tVe K for Our muit be Com|>Ltl€d fro«vi § ^3 7 ) v^-klit -for i|,c 
tfy%j}ulse erf y^oStv oy a.W ovv jijce<i "JiloT-cS Kc otW-.^ ^ ^ /.^^ 

lie cowt^cJirf- -{ov tti« ^wam, tty^traXUxe. Ani )>a.Y-o>v.elTi<: Vie'ijKL 
|crus«mc<j*. (I) aoa «.), \^Fov EX'^mps Set ^ 6;jol 
^"i*?. WIND- PReSSOl?^^" lUe S^rt-act <sf «. voof mtUt,/ 

;^W/^'-T^a^p;/,;^ Q' / '/>(!'" — CO 

O ^ w.«a) ^cr un.t .i ^«<^, ^«i y_ y^^t c.,a;«.L lt,e«Ak- 
^ }, = VO It5.),er s^c^v. ^at(^^, ^ .v,«o.i^„^ ) w, We. 

For OCX 6* /o* /s"* ^0 ^6" So"* 36* Vo° ^S 6c Ss"" 6o* 
^Vf^^*'^ ^'^ '"^ '^'^ ^? i>' ^^.i 3c?./ 33.^ 36./ 38, lt6 l^o. 

ct*t.c {odt,wc V-^oe V, , 

\oatjHiev\ TK& u/otV lost UwovU o{ ^l'/* 3 '^^ oocvcommo. lliejc 



^^'ZO 



^XAKAP/^E Or pADDkE-WHftL 



at? 



YeJisVanceS [3ev SCdowj. C»'^- ^ ovu^r lo^tA ij ^ 

X = lOli:,Jf\!lO =:. :?032^ ji/l^^ , ^zr ^ec . Kevice The )»owcr- 

Ort rViC ^lio|j^ , pos\r»ovi JinJ vclociru oj^ t\Te i>'»ov»vi^ ^oUi/ ^ avid ai 
So OL^On IV) e You^iVin<s5 ©j U j ^.-iyIaC^. I^ \t is ^^oinled cat Uttj €hds 

—"'/-'— —'-rj:.— :- (_H<^.^5^) w;mMscog\ 

"5 ^"*"^-^^j^«" ! ~ — - Ix^Y-f'^^*^ To \We y^ocitx^^ 

wW.e U«<5;t..cl.^al .o.>.),o«e,.r. ^l>v.X„v,..l% W)c«,c« ft,* co.- 

"'"/tit '^""^ "*' ^^^^"-' ^-^-^ 4fta Ul,;-^ 

res^^Un. of Ti^ese resUl^.c.s is c ^.<e -R <x<t,;,^ ,^. Ti,/ l,„e 

AB of i^»>^m«^r^ Cs^l^os/.^ 1i,,e l,^cLj 35,v,.„,r*-.c«<l cO.^^ the 




yiovi^c Bodies isuASusso 




^i)r 




~" eclJiei arc -jormecl -round the ^orvx- 

p. ,- Vesbure j^yom teXJv^a is less tkait 

Morf, rktuur^ini^h^d pre,,ure on BF l\ <ur.^o<^ou,, fcTthe k 

youj sechon the e^Wjement from w),^ck k the af^o/^a! se<:. 
hen )5 s^dJ.n, F.j.,/:;^, ^30^ ^^posiny H^c V.W.^ V ^.^ 

fc.W) «>>— ^«^^ ^'- ^^'-■^-'^^.^«. i. M.. 

It ;» .; eucd«Ht Hxat blufyi^esj of slhn ,ncru.s^s the ^<- 
Udar^ 7,w/, ,^^e /S«,, %l^ffncsi erf hou. 

In «„j eai-c t.)^tY\y^e.\xl sliows H,Ut for ct ^'loei^ l»oJ«,iy», 
-melVica? oiljocd oin ctx'ii c,Ka ivioi/iVa Wxrouok <5<-f}tv:^ t^^ 

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